This book provides a detailed commentary on the classic monograph by Alfred Tarski, and offers a reinterpretation and retranslation of the work using the original Polish text and the English and German translations. In the original work, Tarski presents a method for constructing definitions of truth for classical, quantificational formal languages. Furthermore, using the defined notion of truth, he demonstrates that it is possible to provide intuitively adequate definitions of the semantic notions of definability and denotation and that (...) the notion in a structure can be defined in a way that is analogous to that used to define truth. Tarski’s piece is considered to be one of the major contributions to logic, semantics, and epistemology in the 20th century. However, the author points out that some mistakes were introduced into the text when it was translated into German in 1935. As the 1956 English version of the work was translated from the German text, those discrepancies were carried over in addition to new mistakes. The author has painstakingly compared the three texts, sentence-by-sentence, highlighting the inaccurate translations, offering explanations as to how they came about, and commenting on how they have influenced the content and suggesting a correct interpretation of certain passages. Furthermore, the author thoroughly examines Tarski’s article, offering interpretations and comments on the work. (shrink)

We can distinguish different senses in which a formal language can be said to have been provided with an interpretation. We focus on two: (i) We provide a model (or structure) and a definition of satisfaction and truth in the standard way (ii) We provide a translation into a natural language. We argue that the sentences of a formal language interpreted as in (i) do not have meaning. A formal language interpreted as in (i) models (...) the way the truth of a sentence would be affected by two factors: the interpretation as in (ii) of the language, and a way the world might be. Viewing in this way the relation between interpreting a formal language as in (i) and as in (ii) allows us to justify the conceptual adequacy of the standard model-theoretic definitions of the properties of logical truth and logical consequence. (shrink)

The purpose of this introduction is to give a rough overview of the discussion of the formalization of arguments, focusing on deductive arguments. The discussion is structured around four important junctions: i) the notion of support, which captures the relation between the conclusion and premises of an argument, ii) the choice of a formal language into which the argument is translated in order to make it amenable to evaluation via formal methods, iii) the question of quality criteria (...) for such formalizations, and finally iv) the choice of the underlying logic. This introductory discussion is supplemented by a brief description of the genesis of the special issue, acknowledgements, and summaries of each article. (shrink)

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments (...) translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic. (shrink)

This book presents novel formalizations of three of the most important medieval logical theories: supposition, consequence and obligations. In an additional fourth part, an in-depth analysis of the concept of formalization is presented - a crucial concept in the current logical panorama, which as such receives surprisingly little attention.Although formalizations of medieval logical theories have been proposed earlier in the literature, the formalizations presented here are all based on innovative vantage points: supposition theories as algorithmic hermeneutics, theories of consequence analyzed (...) with tools borrowed from model-theory and two-dimensional semantics, and obligations as logical games. For this reason, this is perhaps the first time that these medieval logical theories are made fully accessible to the modern philosopher and logician who wishes to obtain a better grasp of them, but who has always been held back by the lack of appropriate ‘translations' into modern terms.Moreover, the book offers a reflection on the very nature of logic, a reflection that is prompted by the comparisons between medieval and modern logic, their similarities and dissimilarities. It is thus a contribution not only to the history of logic, but also to the philosophy of logic, the philosophy of language and semantics.The analysis of medieval logic is also relevant for the modern philosopher and logician in that, being the unifying methodology used across all disciplines at that time, logic really provided unity to science. It thus presents a unified model of scientific investigation, where logic plays the aggregating role. (shrink)

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical (...) investigation into conditional connectives may show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

In this paper we propose a way to deal with natural language inference by implementing Modern Type Theoretical Semantics in the proof assistant Coq. The paper is a first attempt to deal with NLI and natural language reasoning in general by using the proof assistant technology. Valid NLIs are treated as theorems and as such the adequacy of our account is tested by trying to prove them. We use Luo’s Modern Type Theory with coercive subtyping as the formal language (...) into which we translate natural language semantics, and we further implement these semantics in the Coq proof assistant. It is shown that the use of a MTT with an adequate subtyping mechanism can give us a number of promising results as regards NLI. Specifically, it is shown that a number of inference cases, i.e. quantifiers, adjectives, conjoined noun phrases and temporal reference among other things can be successfully dealt with. It is then shown, that even though Coq is an interactive and not an automated theorem prover, automation of all of the test examples is possible by introducing user-defined automated tactics. Lastly, the paper offers a number of innovative approaches to NL phenomena like adjectives, collective predication, comparatives and factive verbs among other things, contributing in this respect to the theoretical study of formal semantics using MTTs. (shrink)

Mahayana Texts Translated into Western Languages. A Bibliographical Guide compiled by Peter Pfandt on behalf of the Religionswissenschaftliches Seminar, Bonn University. E. J. Brill, Cologne 1983. xvi + 167pp. DM 27.

Théophile De Donder, a Belgian mathematician born in Brussels, elaborated two important ideas that created a bridge between thermodynamics and chemical kinetics. He invented the concept of the degree of advancement of a reaction, and, in 1922, he provided a precise mathematical form to the already known chemical affinity by translating Clausius’s uncompensated heat into formal language. These concepts merge in an important inequality that was the starting point for the formalization of non-equilibrium thermodynamics. The present article aims (...) to reconstruct how De Donder elaborated his ideas and developed them by exploring his teaching activity and its connection with his scientific production. Furthermore, it emphasizes the role played by the discussions with his disciples who became his collaborators. The paper analyzes De Donder’s efforts in participating in the second Solvay Chemistry Council in 1925 to call the attention of chemists to his mathematical approach. We explain why his work did not receive much attention at the time, and how, despite this, his formalization of chemical affinity became the basis for the birth of the so-called Brussels school of thermodynamics. (shrink)

An Invitation to Formal Reasoning introduces the discipline of formal logic by means of a powerful new system formulated by Fred Sommers. This system, term logic, is different in a number of ways from the standard system employed in modern logic; most striking is its greater simplicity and naturalness. Based on a radically different theory of logical syntax than the one Frege used when initiating modern mathematical logic in the 19th Century, term logic borrows insights from Aristotle's syllogistic, (...) Scholastic logicians, Leibniz, and the 19th century British algebraists. Term logic takes its syntax directly from natural language, construing statements as combinations of pairs of terms, where complex terms are taken to have the same syntax as statements. Whereas standard logic requires extensive 'translation' from natural language to symbolic language, term logic requires only 'transcription' into the symbolic language. Its naturalness is the result of its ability to stay close to the forms of sentences usually found in every day discourse. Written by the founders of the term logic approach, An Invitation to Formal Reasoning is a unique introduction and exploration of this new system, offering numerous exercises and examples throughout the text. Summarising the standard system of mathematical logic to set term logic in context, and showing how the two systems compare, this book presents an alternative approach to standard modern logic for those studying formal logic, philosophy of language or computer theory. Fred Sommers is Professor Emeritus, Brandeis University, USA; George Englebretsen is Professor of Philosophy, Bishop's University, Canada. (shrink)

I assume that the task of natural language semantics is to provide an unambiguous logical language into which natural language can be translated in such a way that the translating expressions display a structure which is isomorphic to the meaning of the translated expressions. Since language is a means of thinking and communicating mental contents, the meanings of singular terms cannot be the individuals of the substratist tradition, because such individuals are not cognizable entities. Thus I propose that the (...) logical language be based on Castaneda's guise theory, according to which singular terms always denote guises, i.e., roughly, bundles of properties. This, I argue, would result in a semantics which is in accordance with projects such as Lakoff's natural logic or Fodor's methodological solipsism. ;I first propose a formal system, GCC, which tries to be as faithful as possible to Castaneda's informal presentation of guise theory. It is therefore characterized by different forms of predication and a distinction between a level of property composition and a level of proposition composition. Such a distinction is dropped in a second system, GF, which presents a more traditional Fregean representation of predication. Yet, GF endorses essential assumptions of guise theory such as the existence of different sameness relations that can provide various interpretations for the English "is". I claim that GF provides more theoretical simplicity than GCC. ;Finally, I show the fruitfulness of the present approach by applying GF to a vast collection of linguistico-philosophical puzzles which includes but is not restricted to those that guise theory was originally designed to address: various versions of Frege's paradox, the paradox of analysis, Quine's puzzle on the number of planets, issues of reidentification and intentional identity, the anaphoric "it" of sentences such as "the lizard's tail fell off but then it grew back," problems connected with the use of "knowing-who ," proper names, indexicals and demonstratives. (shrink)

As a discipline, logic is arguably constituted of two main sub-projects: formal theories of argument validity on the basis of a small number of patterns, and theories of how to reduce the multiplicity of arguments in non-logical, informal contexts to the small number of patterns whose validity is systematically studied . Regrettably, we now tend to view logic 'proper' exclusively as what falls under the first sub-project, to the neglect of the second, equally important sub-project. In this paper, I (...) discuss two historical theories of argument formalization: Aristotle's syllogistic theory as presented in the "Prior Analytics", and medieval theories of supposition. They both illustrate this two-fold nature of logic, containing in particular illuminating reflections on how to formalize arguments . In both cases, the formal methods employed differ from the usual modern technique of translating an argument in ordinary language into a specially designed symbolism, a formal language. The upshot is thus a plea for a broader conceptualization of what it means to formalize. Pode-se dizer que, enquanto disciplina, a lógica é caracterizada por dois subprojetos: teorias formais da validade de argumentos, baseadas em um número reduzido de esquemas e padrões formais, e teorias de como reduzir a multiplicidade de argumentos em contextos informais, não lógicos, ao pequeno número de padrões formais cuja validade é estudada de maneira sistemática no âmbito do primeiro subprojeto. O segundo subprojeto corresponde à noção de formalização de argumentos. Infelizmente, a tendência atual é de considerar como sendo a lógica propriamente dita exclusivamente o que se encaixa no primeiro subprojeto, em detrimento do segundo subprojeto, igualmente importante. Neste artigo, duas teorias históricas sobre a formalização de argumentos são analisadas: a teoria da silogística apresentada por Aristóteles nos "Primeiros Analíticos" e teorias medievais da suposição. Ambas ilustram o caráter duplo da lógica, que envolve dois subprojetos distintos, e contêm reflexões sofisticadas sobre como formalizar argumentos. Em ambos os casos, os métodos formais utilizados se diferenciam dos métodos atuais de tradução de um argumento em linguagem vernacular para um simbolismo especialmente formulado, ou seja, uma linguagem formal. Em conclusão, o artigo pode ser visto como a defesa de uma conceitualização mais abrangente do que significa 'formalizar' um argumento. (shrink)

Recent developments in game theory have shown that the mathematical models of action so widely admired in the study of economics are in fact only particular instantiations of a more general theoretical framework. In the same way that Aristotelian logic was ‘translated’ into the more general and expressive language of predicate logic, the basic action theoretic underpinnings of modern economics have now been articulated within the more comprehensive language of game theory. But precisely because of its greater generality and (...) expressive power, game theory has again revived the temptation to apply formal models of action to every domain of social life. This movement has been fuelled by some notable successes. Game theory has provided useful insights into the logic of collective action in the theory of public goods, and strategic models of voting have illustrated important aspects of institutional decision-making. But this extension of formal models into every area of social interaction has also encountered significant difficulties, despite the fact that contemporary decision theory has weakened its basic assumptions to the point where it teeters constantly on the brink of vacuity. (shrink)

_The Logic of Our Language_ teaches the practical and everyday application of formal logic. Rather than overwhelming the reader with abstract theory, Jackson and McLeod show how the skills developed through the practice of logic can help us to better understand our own language and reasoning processes. The authors’ goal is to draw attention to the patterns and logical structures inherent in our spoken and written language by teaching the reader how to translate English sentences into formal (...) symbols. Other logical tools, including truth tables, truth trees, and natural deduction, are then introduced as techniques for examining the properties of symbolized sentences and assessing the validity of arguments. A substantial number of practice questions are offered both within the book itself and as interactive activities on a companion website. (shrink)

In this paper, I assume, perhaps controversially, that translation into a language of formal logic is not the method by which mathematicians assess mathematical reasoning. Instead, I argue that the actual practice of analyzing, evaluating and critiquing mathematical reasoning resembles, and perhaps equates with, the practice of informal logic or argumentation theory. It doesn’t matter whether the reasoning is a full-fledged mathematical proof or merely some non-deductive mathematical justification: in either case, the methodology of assessment overlaps to (...) a large extent with argument assessment in non-mathematical contexts. I demonstrate this claim by considering the assessment of axiomatic or deductive proofs, probabilistic evidence, computer-aided proofs, and the acceptance of axioms. I also consider Jody Azzouni’s ‘derivation indicator’ view of proofs because it places derivations—which may be thought to invoke formal logic—at the center of mathematical justificatory practice. However, when the notion of ‘derivation’ at work in Azzouni’s view is clarified, it is seen to accord with, rather than to count against, the informal logical view I support. Finally, I pose several open questions for the development of a theory of mathematical argument. (shrink)

David Lewis’s counterpart theory is often seen as involving a radical departure from the standard, Kripke-style semantics for modal logic, suggesting that we are dealing with deeply divergent accounts of our modal talk. However, CT captures but one version of the relevant semantic intuition, and does so on the basis of metaphysical assumptions that are ostensibly discretionary. Just as ML can be translated into a language that quantifies explicitly over worlds, CT may be formulated as a semantic theory in (...) which world quantification is purely metalinguistic. And just as Kripke-style semantics is formally compatible with the doctrine of world-boundedness, a counterpart-based semantics may in principle allow for cases of trans-world identity. In fact, one may welcome a framework that is general enough to include both Lewis’s counterpart-based account and Kripke’s identity-based account as distinguished special cases. There are several ways of doing so. The purpose of this paper is to outline a fully general option and to illustrate its philosophical significance, showing how the large variety of intermediate relations that lie between Lewisian counterparthood and Kripkean identity yield a corresponding variety of modal theories that would otherwise remain uncharted. (shrink)

Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs.

The subject of research in this article is the question of the possibility of formalizing the general theory of systems, that is, turning it into a language for describing systems of any nature with unambiguously defined lexical units and rules. To answer this question, the author considers the phenomenon of semantic indeterminacy of languages, which ensures the flexibility of formed lexical constructions due to the multivalence of lexical units. Also the subject of the research is the practice of (...) quoting out of context – a phenomenon, the admissibility of which is conditioned by the isomorphism of lexical constructions, as well as by the creative nature of the cognitive process, in which the result of cognition is unknown in advance, and thus the change of interpretation of the used concepts is inevitable. The conducted research allows us to state that the general theory of systems cannot be exclusively an applied theory, but should be supplemented with an ontological component. In this case, it becomes a philosophical theory, for which full formalization is impossible without loss of functionality. As a result, general systems theory must inevitably retain a certain semantic uncertainty. This uncertainty, however, can be reduced by translation into universality and generalization of concepts. Besides, it is possible and in some cases necessary to formalize separate components of the general theory of systems, in particular, its ontological component - the metaphysics of material existence. (shrink)

This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...) in logic, by means of ‘translations’ of the medieval logical theories into the modern framework of symbolic logic, i.e. formalizations. One of its conclusions is that, when properly understood within their own framework, the interest of medieval logical theories for modern investigations go beyond mere historical interest, but that a thorough conceptual analysis of such theories must be undertaken in order to avoid conceptual misprojections. While such translations of medieval into modern logic have been attempted before, the approach presented here is innovative in that attention is paid to the similarities as well as to the dissimilarities between the two traditions, and to what can be learned from the medieval masters for modern investigations in logic and semantics. (shrink)

Rather than a simple transfer of words or texts from one language to another, on the model of the bilingual dictionary, translation has become understood as a translingual act of transcoding cultural material--a complex act of communication. Much recent work on translation in history grows out of interest in the effects of European colonialism, especially within Asian studies, where interest has been driven by the contrast between the experiences of China and Japan, which were never formally colonized, and (...) the alternative examples of peoples without strong, centralized states--those of the Indian subcontinent and the Tagalog in the Philippines--who were colonized by European powers. This essay reviews several books published in recent years, one group of which share the general interpretation that colonial powers forced their subjects to "translate" their local language, sociality, or culture into the terms of the dominant colonial power: because the colonial power controls representation and forces its subjects to use the colonial language, it is in a position to construct the forms of indigenous and subject identity. The other books under review here are less concerned with power in colonial situations than with the fact of different languages, cultures, or practices and the work of "translating" between the two--particularly the efforts of indigenous agents to introduce European ideas and institutions to their respective peoples. (shrink)

In this textbook on elementary logic the authors present a rigorous treatment of first the propositional, and then the predicate calculi. The first two chapters deal with the former topic exclusively: there is much emphasis on translation of ordinary-language sentences into logic and testing their validity; also a proof notation consisting of nested boxes, similar to the Fitch subproof technique, is introduced and used. The third and fourth chapters are concerned with quantification theory in application to language analysis; (...) the next chapter discusses more theoretical topics including a proof procedure for formulae in prenex normal form and decision procedures for restricted classes of such formulae. Identity is treated next, with the following chapter on definite descriptions. The eighth chapter is more formal in approach and has as its subject the abstract approach to logical systems: the notion of the extension of a theory is introduced at this stage; two examples of formal theories—the theory of commutative ordered fields, and that of real numbers—are presented and come under extensive elaboration. The last chapter discusses variable-binding operations and presents the theory of convergence of series as an example of such a theory with these operations. Each chapter has numerous exercises, and most have historical remarks and lists of theorems of that chapter.—P. J. M. (shrink)

Dorion Cairns’ translations of Husserl have been acclaimed for their exactness and rigor. Even in the most complex passages of Formal and Transcendental Logic, for example, no emphasis or detail is missed, and one can use the translation with great confidence. One of the principles guiding Cairns’ translation is stated in the Preface to this Guide: "So far as possible someone who translates such writings as Husserl’s into another language should always render the same German expression (...) by the same expression in the other language, and different German expressions by different expressions in the other language." In carrying out this injunction himself, Cairns compiled a detailed glossary of German-English equivalents and this book is its final codification. It can be very useful not only for translation but for reading Husserl in German, since some parts or volumes of Husserliana will probably not be translated. (shrink)

This accessible, SHORT introduction to symbolic logic includes coverage of sentential and predicate logic, translations, truth tables, and derivations. The author's engaging style makes this the most informal of introductions to formal logic. Topics are explained in a conversational, easy-to-understand way for readers not familiar with mathematics or formal systems, and the author provides patient, reader-friendly explanations—even with the occasional bit of humour. The first half of the book deals with all the basic elements of Sentential Logic: the (...) five truth-functional connectives, formation rules and translation into this language, truth-tables for validity, logical truth/falsity, equivalency, consistency and derivations. The second half deals with Quantifier Logic: the two quantifiers, formation rules and translation, demonstrating certain logical characteristics by “Finding an Interpretation” and derivations. There are plenty of exercises scattered throughout, more than in many texts, arranged in order of increasing difficulty and including separate answer keys. (shrink)

Following Richard M. Hare1 I think that we use practical sentences as decision criteria. We understand their meaning if we know what decision to take according to them. But it is not clear, how exactly decision criteria are related to decisions and how they function as criteria. To fully understand this role, we need a formal semantics of practical sentences. For this I have to introduce a formal language and give an interpretation of it. This language has to (...) be constructed in such a way that a translation into ordinary language is always possible in principle. Thus, we make sure that our semantics and logic will have an impact on the solution of concrete practical problems. According to this program I will first introduce the formal language ‘LP1’. To give an interpretation of it I will then clarify what a decision is and show how practical sentences function as decision criteria. On this basis I give an interpretation of the primitive two-place operator ‘PT p,q’ and the one-place operator ‘VTp’. I further argue that we make meta-decisions concerning the application of first-order decision-criteria. This allows me to introduce a new concept of practical validity, which differs radically from the concept of truth. Using this concept, I then give an interpretation of the deontic operators ‘OTp’, ‘FTp’, ‘ATp’ and ‘ITp’. The concept of practical validity makes it also possible to introduce practical logical connectors and mixed logical connectors on the basis of practical or mixed value tables. These connectors are used – among others – in bridge-principles, which play an important role in ethical and juridical theories. Finally, I shortly explain the semantics of the main kinds of practical sentences, i.e. value judgments, imperatives, norms and intentions, and I argue that we need a deontic logic in order to use practical sentences in a correct way. (shrink)

The aim of the paper is to compare the role played by logical analysis in Wittgenstein’s Tractatus logico-philosophicus and Russell’s On Denoting. Whereas in Russell’s work it is an important element of his argument in support of description theory, in his pupil’s it does not function this way. Russell, while analysing various propositions, including descriptions translates them into formal language, indicating that those propositions, despite the appearances, in fact do not denote. Logical analysis shall be a tool decisive (...) in favour of Russell’s thesis. Wittgenstein similarly analyses some troublesome propositions and claims that they are meaningless. The difference is that Russell’s final conclusion is derived from logical analysis, whereas Wittgenstein’s from pure speculation. In Tractatus logico-philosophicus logical analysis is not a method thanks to which the author gets certain result, just as it was the case with his teacher and his On Denoting. In Wittgenstein’s early philosophy logical analysis concerns just a few technical problems connected only to some ideas from Principia mathematica, and not to the main subject of his work, which is the analysis of philosophical theses. (shrink)

More than 50 years ago, Bongard introduced 100 visual concept learning problems as a challenge for artificial vision systems. These problems are now known as Bongard problems. Although they are well known in cognitive science and artificial intelligence, only very little progress has been made toward building systems that can solve a substantial subset of them. In the system presented here, visual features are extracted through image processing and then translated into a symbolic visual vocabulary. We introduce a (...) class='Hi'>formal language that allows representing compositional visual concepts based on this vocabulary. Using this language and Bayesian inference, concepts can be induced from the examples that are provided in each problem. We find a reasonable agreement between the concepts with high posterior probability and the solutions formulated by Bongard himself for a subset of 35 problems. While this approach is far from solving Bongard problems like humans, it does considerably better than previous approaches. We discuss the issues we encountered while developing this system and their continuing relevance for understanding visual cognition. For instance, contrary to other concept learning problems, the examples are not random in Bongard problems; instead they are carefully chosen to ensure that the concept can be induced, and we found it helpful to take the resulting pragmatic constraints into account. (shrink)

This book is an introduction to elementary logic (classical propositional and first-order logic), comprising brief summaries of the basics of elementary logic, with the emphasis on typical questions and procedure descriptions and with a large number of corresponding exercises and problems. Solutions are given for each problem and exercise, often with commentaries. The first part, Basics of Logic, deals with (a) formal language, models, Venn diagrams for sentences, and translation from natural into formal language and vice (...) versa, (b) deduction and refutation methods in the format of natural deduction (Fitch and Suppes-Lemmon styles), tableau system and Venn diagrams, and (c) basic logical properties and relations (consistency, validity, consequence, equivalence, various types of opposition, logical completeness and independency, relationship between syntax and semantics). The second part, Logic in Understanding and Analysis, introduces into (a) logical approach to problem solving in concrete situations and events as presented in brief tales and anecdotes, (b) discovering the meaning, and reconstruction of logical interconnections, in ordinary, scholarly and philosophical texts, (c) application of already mastered logical tools in examining and defining further theoretical (logical, scientific) concepts and in building formal languages. The shorter third part, From the Traditional Logic, is dedicated to the traditional logic of concepts, judgements and syllogisms, largely with the use of Venn diagrams. (shrink)

Clear focus on its application of formal logic to ordinary English is the most distinctive feature of this textbook for the introductory course in deductive logic. Great care is taken with the appropriate translation into logical languages of ordinary English sentences. Evaluation of these translations promotes a more effective use of ordinary language. The Principles of Deductive Logic presents symbolic logic in a fuller and more leisurely fashion than other introductory textbooks. Early chapters cover informal material, (...) including definition and informal fallacies. The remainder of the text is devoted to the treatment of four distinct artificial languages. The Categorical language is the language of syllogistic logic. The Extended Categorical language enriches this first language with the symbolic connectives for conjunction and negation. The Propositional Connective language and the First-Order language are the two basic languages of modern logic. Each language is accompanied by a deductive system, and is used as an instrument for exploring ordinary language, including ordinary arguments The book contains a large number of exercises whose answers are supplied in the back of the book, and many more that can be assigned as homework. A solution’s manual is available to instructors upon their request. The request must be written on college or university letterhead. (shrink)

WHAT do we mean by saying that a being, God for example, is omniscient? One way of answering this question is to translate ‘God is omniscient’ into some slightly more formalised language than colloquial English, e.g. one with variables of a number of different types, including variables replaceable by statements, and quantifiers binding thes.

In lieu of an abstract, here is a brief excerpt of the content:Review of Stephen Phillips' Jewel of Reflection on the Truth about Epistemology:A Complete and Annotated Translation of the Tattva-cintā-maṇiMichael Williams (bio)Stephen Phillips presents a translation and commentary on Gaṅgeśa Upādhyāya's Tattvacintāmaṇi, which is widely regarded as the foundational text of the Navya-Nyāya tradition. The importance of Gaṅgeśa's work to subsequent philosophy in India can hardly be overstated. In the centuries after his death, countless commentaries and dissertations (...) were written on the Tattvacintāmaṇi by Nyāya scholars in Mithila and Bengal. Recent [End Page 510] scholarship (David and Duquette 2021) has highlighted how the work of the Navya-Naiyāyikas came to influence intellectuals from all over the Indian subcontinent. The theories of Gaṅgeśa and his followers shaped discussions in diverse scientific fields, including Vedānta, Mīmāṃsā, grammatical science, and literary theory.Despite its pervasive impact on Indian thought, Navya-Nyāya has frequently been portrayed in a negative light by scholars. The Indologist Arthur Berriedale Keith (1921, p. 35) described the commentaries on Gaṅgeśa's work as "a vast mass of perverted ingenuity worthy of the most flourishing days of mediaeval scholasticism." Meanwhile, Swami Vivekananda bemoaned the "never ending Avacchinnas and Avacchedakas" of Navya-Nyāya prose.1Jonardon Ganeri (2011) has discussed how these negative stereotypes reach back to the political agenda of the British colonial government in India during the nineteenth century, and his work highlights the vitality and diversity of the discussion of metaphysics in the Bengali tradition of Navya-Nyāya. Nevertheless, there is no denying that much Navya-Nyāya work is extremely difficult to discuss and translate comprehensibly. Many scholars still think of Navya-Nyāya works as untranslatable, at least in the sense that their meaning could not be effectively communicated to a modern audience who are not already deeply familiar with the tradition. This would be tragic, given the potential of Navya-Nyāya philosophy to contribute to the growing cross-cultural conversation in philosophy.Phillips is the first scholar to translate the entire Tattvacintāmaṇi into another language. His work attempts to communicate the foundational text of the Navya-Nyāya tradition to a broad audience. In his introduction, Phillips says that his work aims to speak to analytic philosophers, Sanskritists, and "specialists whose interests span issues in contemporary philosophy and Gaṅgeśa's achievements" (2020, vol. 1, p. 1). Phillips worked with the late Ramanuja Tatacharya to read the Tattvacintāmaṇi's chapters on perception and inference. Tatacharya was recognized as one of the leading experts on Navya-Nyāya philosophy in the world during his lifetime, and Phillips' translation distils many of his insights into the text.Phillips' goal is to translate the Tattvacintāmaṇi into lucid English. He eschews what he terms the "error of literalism" (2020, 1:xvi), instead using idiomatic translations that draw on concepts from contemporary analytic philosophy. Unlike Daniel Ingalls (1951) and Cornelius Goekoop (1967), Phillips uses formalization in Property Predicate Logic comparatively rarely, deploying it selectively in contexts such as the discussion of the nature of pervasion (the Vyāptivāda) and the discussion of the "inferential undercutter" (the Upādhivāda), for instance. The introduction to the work is extremely clear and explains the translation using terms of modern analytic philosophy. Phillips presents a perspicuous introduction to the theory of inference, [End Page 511] which is necessary to understanding Gaṅgeśa's work, which constantly employs inferential arguments.Phillips' introductions to the individual chapters of the text are also very illuminating, and often contain original insights into the philosophy of the Tattvacintāmaṇi. For instance, his introduction to the Īśvaravāda argues, contra John Vattanky ([1989] 2011), that Gaṅgeśa himself was not entirely persuaded of the strength of the proofs for the existence of god (īśvara) that he puts forward in that chapter. Phillips argues that Gaṅgeśa may actually have sympathized to some extent with the Mīmāṃsā views he ultimately critiques there, detecting on Gaṅgeśa's part a "sympathy for certain atheistic... (shrink)

This experimental study provides further support for a theory of meaning first put forward by Bar-Hillel and Carnap in 1953 and foreshadowed by Asimov in 1951. The theory is the Popperian notion that the meaningfulness of a proposition is its a priori falsity. We tested this theory in the first part of this paper by translating to logical form a long, tightly written, published text and computed the meaningfulness of each proposition using the a priori falsity measure. We then selected (...) the top propositions—by a priori falsity—and strung them together to form ad hoc abstracts and compared these abstracts with the published summary. The results were startling: translation to logical form, followed by application of the Asimovian idea and Bar-Hillel/Carnap mathematics as elaborated into an AI/NLP proposal in Fulda (1986, 1988), produced excellent abstracts, thereby providing a proof-of-concept that merely by knowing the logical form of long text passages, one can produce reasonable abstracts of them—without actually understanding the text. We here report on a second experiment analyzing, in the exact same manner, the correspondence that followed the published text of the first experiment. While the results of this confirming experiment are less startling, they nevertheless provide additional confidence in the promise of the technique. In other words, were the results of these two experiments to generalize, that would show that logical form captures much more semantics than has heretofore been considered likely. Far from (as is commonly supposed) being merely the syntactical rewrite of text into formal notation, translation to logical form, even when undertaken with almost no knowledge about the particular predicates, individual constants, or other objects referred to in that form, might capture the core of the meaning in some important sense. -/- Note: There is a key difference in the /style/ of the texts analyzed in I and II in this long paper, divided into two only for practical reasons—space; the first text analyzed is written in a tight mathematical style, while the second is written in the discursive style of philosophy. -/- Finally, the unusual (for me) length of this two-part paper is justified by its being data-driven. (shrink)

There are legitimate worries about gaps between scientific evidence of brain states and function (for example, as evidenced by fMRI data) and legal criteria for determining criminal culpability. In this paper I argue that behavioral evidence of capacity, motive and intent appears easier for judges and juries to use for purposes of determining criminal liability because such evidence triggers the application of commonsense psychological (CSP) concepts that guide and structure criminal responsibility. In contrast, scientific evidence of neurological processes and function (...) – such as evidence that the defendant has a large brain tumor – will not generally lead a judge or jury to directly infer anything that is relevant to the legal determination of criminal culpability . (Vincent 2008) In these cases, an expert witness will be required to indicate to the fact-finder what this evidence means with regard to mental capacity; and then another inference will have to be made from this possible lack of capacity to the legal criteria for guilt, cast in CSP terms.<br><br>To reliably link evidence of brain function and structure and assessment of criminal responsibility, we need to re-conceptualize the mental capacities necessary for responsibility, particularly those that are recognized as missing or compromised by the doctrines of “legal capacity” (Hart 1968) and “diminished capacity.” I argue that formulating these capacities as executive functions within the brain can provide this link. I further claim that it would be extremely useful to consider evidence of executive function as related to the diminished capacity doctrine at sentencing. This is because it is primarily at this stage in criminal proceedings where the use of the diminished capacity doctrine is most prevalent, as evidenced by the recent Supreme Court cases of Atkins v. Virginia (536 U.S. 304 (2002)) and Roper v. Simmons (543 U.S. 551 (2005)).<br>. (shrink)

This is a thesis in formal semantics. It consists of two parts corresponding to the distinction, due to Richard Montague, between universal grammar and specific semantic theories. The first part concerns universal grammar and is intended to provide a precise and unified conceptual framework within which different theories of formal semantics can be represented and compared. ;The second part of the thesis is concerned with intensional logic, i.e., with the logical analysis of discourse involving so called oblique contexts. (...) These contexts are characterized by the apparent failure of certain classically valid principles of substitutivity. Two kinds of reactions among logicians to the appearance of oblique contexts in natural languages are distinguished: (1) the intensional point of view, according to which oblique contexts are seen as genuine counterexamples to classical logic and to the related semantical principle of extensionality: the principle that the denotation of an expression is a function of the denotations of its parts; and (2) the extensional point of view, according to which the conflict between oblique contexts and classical logic is only apparent. The extensional point of view therefore calls for analyses of oblique contexts that preserve the laws of classical logic and the principle of extensionality. In this thesis, we are concerned with the precise formulation of and comparison between different programs for the formal semantic representation of oblique contexts. In Chapter 5, we are concerned with Church's program of representing oblique contexts within a formal language whose semantics is fully extensional and based on Frege's distinction between sense and denotation. The ambiguity between the "direct" and "indirect" denotation of an expression A is avoided by letting A be replaced in oblique contexts by an expression which denotes A's ordinary sense. We provide a possible-worlds semantics for a version of Church's formal language with the following features: (i) Objectual quantification into oblique constructions is accounted for. The treatment of quantification requires for each entity x an essence of x, by which we mean a sense which determines x in those worlds in which x exists and is undefined in all other worlds. (ii) The variables range over actually existing entities only. It is allowed that entities of certain types are contingent, i.e., the same entity may exist in one world and fail to exist in other worlds. (iii) In order to combine a proper treatment of the cross-world identification of functions with varying domains, partial functions are allowed. (iv) Senses are allowed to be partially defined. For example, the sense of a proper name is undefined in a world in which the denotation of the name does not exist. (v) Senses of functions from objects of type a to objects of type b are identified with functions from senses of objects of type a to senses of objects of type b. In Chapters 6 and 7, we pursue the Russellian Alternative in intensional semantics, where a sense/denotation distinction is avoided. Apparent failures of substitutivity principles for singular terms are explained along the lines of Russell's theory of definite descriptions. Failures of substitutivity of coextensional sentences and predicates are explained by Russell's doctrine that sentences and predicate denote propositions and propositional functions , respectively. Russellian semantics is fully extensional in the sense that the Russellian denotation of a designator is a function of the Russellian denotations of its parts. In Chapter 6, a theory of Russellian propositions is developed within set theory. This theory is then applied in Chapter 7 to the task of providing a set-theoretic semantics for Russellian type theory. (shrink)

Excerpt from The Mathematical Psychology of Gratry and Boole: Translated From the Language of the Higher Calculus Into That of Elementary Geometry Dear Dr. Maudsley, - You have often asked me to explain, for students unaquainted with the Infinitesimal Calculus, certain doctrines expressed in terms of that Calculus by P. Gratry and my late husband. That you permit me to dedicate my attempt to you will, at least, be a guarantee that the main ideas of mathematical psychology are based, (...) not on mystic dreams, but on scientific induction. I am glad of this opportunity of expressing to you my gratitude, both for your published works, and for much personal kindness to myself. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

In his recent attempt to make democracy more politically hospitable to religion, Habermas calls for the potential contributions of religion to democratic politics not to be neglected. He simultaneously calls for translating religious meanings into neutral reasons as a way of including them at the level of formal politics and for maintaining the necessity of an institutional translational proviso to immunize the neutral character of the state. This article presents three arguments. First, what Habermas effectively calls for is (...) not conventional translation in which meaning is transferred from one language (signification system) into another. Rather, his call is for an anasemic translation which is an operation of de-signification of the truth contents of religious contributions and then a re-signification. Second, because Habermas calls for translation, he necessarily runs into the aporia of translation in the sense that certain aspects of religion are untranslatable into his generally acceptable language. Therefore, Habermas’ translation proviso creates an asymmetry between religious and non-religious citizens, which is detrimental to the conditions of political legitimacy. Third, it is suggested that to address this problem the citizens must adopt an ethos of hospitality toward the untranslatable of religion as part of the conditions of political legitimacy. (shrink)

i) We show for each context-free language L that by considering each word of L as a structure in a natural way, one turns L into a finite union of classes which satisfy a finitary analog of the characteristic properties of complete universal first order classes of structures equipped with elementary embeddings. We show this to hold for a much larger class of languages which we call free local languages. ii) We define local languages, a class (...) of languages between free local and context-sensitive languages. Each local language L has a natural extension L ∞ to infinite words, and we prove a series of "pumping lemmas", analogs for each local language L of the "uvxyz theorem" of context free languages: they relate the existence of large words in L or L ∞ to the existence of infinite "progressions" of words included in L, and they imply the decidability of various questions about L or L ∞ . iii) We show that the pumping lemmas of ii) are independent from strong axioms, ranging from Peano arithmetic to ZF + Mahlo cardinals. We hope that these results are useful for a model-theoretic approach to the theory of formal languages. (shrink)

What is the meaning of language expressions and how to compute or calculate it? In this paper, we give an answer to this question by analysing the meanings of aspects and tenses in natural languages inside the formal model of an grammar of applicative, cognitive and enunciative operations , using the applicative formalism, functional types of categorial grammars and combinatory logic . In the enunciative theory and following , an utterance can be decomposed into two components: a (...) modus and a dictum . In GRACE, the modus is a complex operator applied to a proposition and is generated from more elementary operators of the categories of tense, aspect, and modality. The dictum is a proposition generated by a predicative relation. In this way, we can attribute a semantic meaning to different grammatical aspecto-temporal operators. The applicative expressions of CL can be easily translated into a functional programming language such as HASKELL or CAML. (shrink)

It is argued that the blind ascriptive role for the word true, its use, that is, in conjunction with descriptions of classes of sentences or with proper names of sentences (but not quote-names), is one which applies indiscriminately to sentences regardless of whether these are in languages we speak, can understand, or can translate into sentences that we do speak (and understand). Formal analogues of the ordinary word true as they arise in Tarskis seminal work, and in (...) others, cannot replicate this essential role of the ordinary word true. (shrink)

It is argued that the blind ascriptive role for the word "true", its use, that is, in conjunction with descriptions of classes of sentences or with proper names of sentences, is one which applies indiscriminately to sentences regardless of whether these are in languages we speak, can understand, or can translate into sentences that we do speak. Formal analogues of the ordinary word "true" as they arise in Tarski's seminal work, and in others, cannot replicate this essential (...) role of the ordinary word "true". (shrink)

The article considers Jürgen Habermas's views on the relationship between postmetaphysical philosophy and religion. It outlines Habermas's shift from his earlier, apparently dismissive attitude towards religion to his presently more receptive stance. This more receptive stance is evident in his recent emphasis on critical engagement with the semantic contents of religion and may be characterized by two interrelated theses: the view that religious contributions should be included in political deliberations in the informally organized public spheres of contemporary democracies, though translated (...) into a secular language for the purposes of legislation and formal decision making and the view that postmetaphysical philosophy should seek to salvage the semantic contents of religious traditions in order to supply the evocative images, exemplary figures, and inspirational narratives it needs for its social and political projects. With regard to, it argues that the translation requirement impairs the political autonomy of religious believers and other metaphysically inclined citizens, suggesting that this difficulty could be alleviated by making a distinction between epistemologically authoritarian and non-authoritarian religious beliefs. With regard to, it argues that the salvaging operation is not as straightforward as Habermas seems to suppose and that social and political philosophy may not be able to tap the semantic power of religious traditions without relying on metaphysical assumptions; it concludes that, here, too, a distinction between authoritarian and non-authoritarian approaches to knowledge and validity may be useful. (shrink)

Natural languages exhibit a great variety of grammatical paradigms. For instance, in English verbs are grammatically marked for tense, whereas in the tenseless Eskimo-Aleut language Kalaallisut they are marked for illocutionary mood. Although time is a universal dimension of the human experience and speaking is part of that experience, some languages encode reference to time without any grammatical tense morphology, or reference to speech acts without any illocutionary mood morphology. Nevertheless, different grammatical systems are semantically parallel in certain (...) respects. Specifically, I propose that English tenses form a temporal centering system, which monitors and updates topic times, whereas Kalaallisut moods form a modal centering system, which monitors and updates modal discourse referents. To formalize these centering parallels I define a dynamic logic that represents not only changing information but also changing focus of attention in discourse (Update with Centering, formalizing Grosz et al 1995). Different languages can be translated into this typed logic by directly compositional universal rules of Combinatory Categorial Grammar (CCG) The resulting centering theory of tense and illocutionary mood draws semantic parallels across different grammatical systems. The centering generalizations span the extremes of the typological spectrum, so they are likely to be universal. In addition, the theory accounts for the translation equivalence of tense and illocutionary mood in a given utterance context. Following Stalnaker (1978) I assume that the very act of speaking up has a ‘commonplace effect’ on the context. It focuses attention on the speech act and thereby introduces default modal and temporal topics. These universal defaults complement language-specific grammars, e.g. English tenses and Kalaallisut moods. In a given utterance context the universal discourse-initial defaults plus language-specific grammatical marking may add up to the same truth conditions.. (shrink)

Wolff's book defends the Kantian idea of a "general logic" whose principles underlie special systems of deductive logic. It thus undermines "logical pluralism," which tolerates the co-existence of divergent systems of modern logic without asking for consistent common principles. Part I of Wolff’s book identifies the formal language in which the most general principles of logic must be expressed. This language turns out to be a version of syllogistic language already used by Aristotle. The universal validity of logical principles, (...) as well as the translatability of other logical languages into this language, are shown to depend only on the meanings of its logical vocabulary. Part II of the book answers the metalogical question concerning the deductive relation between general logic and special logical systems, which also have their own (less general) principles. This part identifies the rules according to which logical rules can be derived from principles. The main result of the book is that the highest principles of logic and metalogics are provided by the syllogistic, when properly understood. (shrink)

‘Language and End Time’ is a translation of Sections I, IV and V of ‘Sprache und Endzeit’, a substantial essay by Günther Anders that was published in eight instalments in the Austrian journal FORVM from 1989 to 1991. The original essay was planned for inclusion in the third volume of The Obsolescence of Human Beings. ‘Language and End Time’ builds on the diagnosis of ‘our blindness toward the apocalypse’ that was advanced in the first volume of The Obsolescence in (...) 1956. The essay asks if there is a language that is capable of making us fully comprehend the looming ‘man-made apocalypse’. In response to this, it offers a critique of philosophical jargon and of the putatively ‘objective’ language of science, which are both dismissed as unsuitable. Sections I, IV and V introduce this core problematic. The selection of this text for inclusion in this special journal issue responds to present-day realities that inscribe Anders’s reflections on nuclear science and the nuclear situation into new contexts. The critique that ‘Language and End Time’ advances resonates with the way in which the decisions of a few companies and individuals are shaping the future of life on earth. At the same time, the wider stakes of Anders’s turn against the language employed by scientists are newly laid bare by the realities and politics of climate change and fake news. In this new context, the language of science is all too readily dismissed as if it were a mere idiom that can be ignored without consequence. It is against the backdrop of a future that is, if anything, more uncertain than at the time of Anders’s writing, that the essay’s reflections on popularisation, the limits of language and the nature of truth gain added significance. (shrink)

Arbitrary symbolism is a linguistic doctrine that predicts an orthogonal relationship between word forms and their corresponding meanings. Recent corpora analyses have demonstrated violations of arbitrary symbolism with respect to concreteness, a variable characterizing the sensorimotor salience of a word. In addition to qualitative semantic differences, abstract and concrete words are also marked by distinct morphophonological structures such as length and morphological complexity. Native English speakers show sensitivity to these markers in tasks such as auditory word recognition and naming. One (...) unanswered question is whether this violation of arbitrariness reflects an idiosyncratic property of the English lexicon or whether word concreteness is a marked phenomenon across other natural languages. We isolated concrete and abstract English nouns, and translated each into Russian, Arabic, Dutch, Mandarin, Hindi, Korean, Hebrew, and American Sign Language. We conducted offline acoustic analyses of abstract and concrete word length discrepancies across languages. In a separate experiment, native English speakers with no prior knowledge of these foreign languages judged concreteness of these nouns. Each naïve participant heard pre-recorded words presented in randomized blocks of three foreign languages following a brief listening exposure to a narrative sample from each respective language. Concrete and abstract words differed by length across five of eight languages, and prediction accuracy exceeded chance for four of eight languages. These results suggest that word concreteness is a marked phenomenon across several of the world's most widely spoken languages. We interpret these findings as supportive of an adaptive cognitive heuristic that allows listeners to exploit non-arbitrary mappings of word form to word meaning. (shrink)

In this article, I develop three conceptual innovations within the area of formal metatheory, and present a computer program, called Reconstructor, that implements those developments. The first development consists in a methodology for testing formal reconstructions of scientific theories, which involves checking both whether translations of paradigmatically successful applications into models satisfy the formalisation of the laws, and also whether unsuccessful applications do not. I show how Reconstructor can help carry this out, since it allows the end-user (...) to specify a formal language, input axioms and models formulated in that language, and then ask if the models satisfy the axioms. The second innovation is the introduction of incomplete models (for which the denotation of some terms is missing) into scientific metatheory, in order to represent cases of missing information. I specify the paracomplete semantics built into Reconstructor to deal with sentences where denotation failures occur. The third development consists in a new way of explicating the structuralist notion of a determination method, by equating them with algorithms. This allows determination methods to be loaded into Reconstructor and then executed within a model to find out the value of a previously non-denoting term (i.e. it allows the formal reconstruction to make predictions). This, in turn, can help test the reconstruction in a different way. Finally, I conclude with some suggestions about additional uses the program may have. (shrink)

Access to legal information is fundamental to access to justice. Yet accessibility refers not only to making legal documents available to the public, but also rendering legal information comprehensible to them. A vexing problem in bringing legal information to the public is how to turn formal legal documents such as legislation and judgments, which are often highly technical, to easily navigable and comprehensible knowledge to those without legal education. In this study, we formulate a three-step approach for bringing legal (...) knowledge to laypersons, tackling the issues of navigability and comprehensibility. First, we translate selected sections of the law into snippets (called CLIC-pages), each being a small piece of article that focuses on explaining certain technical legal concept in layperson’s terms. Second, we construct a Legal Question Bank, which is a collection of legal questions whose answers can be found in the CLIC-pages. Third, we design an interactive CLIC Recommender. Given a user’s verbal description of a legal situation that requires a legal solution, CRec interprets the user’s input and shortlists questions from the question bank that are most likely relevant to the given legal situation and recommends their corresponding CLIC pages where relevant legal knowledge can be found. In this paper we focus on the technical aspects of creating an LQB. We show how large-scale pre-trained language models, such as GPT-3, can be used to generate legal questions. We compare machine-generated questions against human-composed questions and find that MGQs are more scalable, cost-effective, and more diversified, while HCQs are more precise. We also show a prototype of CRec and illustrate through an example how our 3-step approach effectively brings relevant legal knowledge to the public. (shrink)