One of three distinct approaches to his famous ‘Trust’ argument, this paper written by Garfinkel in 1960, and never before published, proposed a rethinking of rules, games and linguistic classifications in interactional terms consistent with Wittgenstein’s language games. Garfinkel had been working in collaboration with Parsons since 1958 to craft an approach to culture that would replace conceptual classification with the constitutive expectancies of interaction and systems of interaction. The argument challenged the work of cultural anthropologists influenced by zoology and (...) biology, who called themselves ‘ethnoscientists’ and studied culture in terms of linguistic classification systems. Garfinkel had proposed an alternative sociological ‘ethnoscience’ of culture and language that would focus on how culture was made, on how linguistic events are achieved, and on the rules of their making. This ‘Language Games’ approach followed Wittgenstein in seeking what Garfinkel called a literal description of cultural/linguistic events: meaning by ‘literal’, a step-by-step account of the constitutive and preferred rules participants use to create a recognizable event-in-a-language. Made famous three years later in version associated with Schutz, Garfinkel’s Trust argument also appears in a 1962 text (Parsons’ Primer, published in 2019) in a version built on Parsons. (shrink)

In this paper, we discuss some formal properties of the model ofbidirectional Optimality Theory that was developed inBlutner (2000). We investigate the conditions under whichbidirectional optimization is a well-defined notion, and we give aconceptually simpler reformulation of Blutner's definition. In thesecond part of the paper, we show that bidirectional optimization can bemodeled by means of finite state techniques. There we rely heavily onthe related work of Frank and Satta (1998) about unidirectionaloptimization.

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different (...) approaches to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence and psychology, deals with the questions of how such conditionals can be best represented and how these conditionals can model human reasoning. On the other hand, findings in the (...) psychology of reasoning, such as those in the Suppression Task, have led to a paradigm shift from the monotonicity assumptions in human inferences towards nonmonotonic reasoning. Nonmonotonic reasoning is sensitive for information change, that is, inferences are drawn cautiously such that retraction of previous information is not required with the addition of new information. While many formalisms of nonmonotonic reasoning have been proposed in the field of Artificial Intelligence, their capability to model properties of human reasoning has not yet been extensively investigated. In this paper, we analyzed systematically from both a formal and an empirical perspective the power of formal nonmonotonic systems to model possible explicit defeaters, as in the Suppression Task, and more implicit conditional rules that trigger nonmonotonic reasoning by the keywords in such rules. The results indicated that the classical evaluation for the correctness of inferences has to be extended in the three major aspects regarding the inference system, the knowledge base, and possible assumed exceptions for the rule. (shrink)

En este trabajo se define formamente el concepto de representacion en química utilizando homomorfismos desde estructuras algebraicas, que llamamos sistemas de tipo C, en otras estructuras especiales de símbolos muy relacionados con los que son habituales en la qímica experimental. Para la definicion de los sistemas de tipo C se ha seleccionado un conjunto minimo de relaciones y funciones, que son necesarias para expresar proposiciones significativas en química. Tambien se define un lenguaje formal de primer orden adecuado a los (...) sistemas de tipo C, que llamamos L(C). EI resultado principal que se demuestra es que toda representación que verifica las mismas sentencias de L(C) que un sistema de tipo C, es necesariamente isomorfo a él. Se concluye por lo tanto que puede existir un problema linguístico subyacente en la aplicacion que de la mecaníca cuántica se hace en la química teórica.The concept of representation in chemistry bas been formallv defined by means of homomorphisms from algebraical structures, which we call type-C systems, to some special sets of symbols which can be related to the symbols ordinarily used in experimental chemistry. A minimum number of relations and functions, which would suffice to express significant propositions in chemistry, have been chosen to define type-C systems. A first order formal language L(C) adequate to type-C systems has been defined. It has been shown that each representation that verifies the same sentences of L(C) as a type-C system is necessarily isomorphic to it. It is concluded that a systematic study of the representation problem in chemistry is in order because a deep language problem underlies the application of quantum mechanies to chemical problems. (shrink)

Words associated with perceptually salient, highly imageable concepts are learned earlier in life, more accurately recalled, and more rapidly named than abstract words (R. W. Brown, 1976; Walker & Hulme, 1999). Theories accounting for this concreteness effect have focused exclusively on semantic properties of word referents. A novel possibility is that word structure may also contribute to the effect. We report a corpus-based analysis of the phonological and morphological structures of a large set of nouns with imageability ratings (N (...) = 2,023). High- and low-imageability nouns differed by length, etymology, prosody, affixation, phonological neighborhood density, and rates of consonant clustering. On average, nouns denoting abstract concepts were longer, more derivationally complex, and emerged in English from a different distribution of languages than did concrete nouns. We address implications for interactivity of word form and meaning as pertain to theories of word concreteness, lexical acquisition, and word processing. (shrink)

Words associated with perceptually salient, highly imageable concepts are learned earlier in life, more accurately recalled, and more rapidly named than abstract words (R. W. Brown, 1976; Walker & Hulme, 1999). Theories accounting for this concreteness effect have focused exclusively on semantic properties of word referents. A novel possibility is that word structure may also contribute to the effect. We report a corpus-based analysis of the phonological and morphological structures of a large set of nouns with imageability ratings (N (...) = 2,023). High- and low-imageability nouns differed by length, etymology, prosody, affixation, phonological neighborhood density, and rates of consonant clustering. On average, nouns denoting abstract concepts were longer, more derivationally complex, and emerged in English from a different distribution of languages than did concrete nouns. We address implications for interactivity of word form and meaning as pertain to theories of word concreteness, lexical acquisition, and word processing. (shrink)

Neural networks are widely used in systems of artificial intelligence, but due to their black box nature, they have so far evaded formal analysis to certify that they satisfy desirable properties, mainly when they perform critical tasks. In this work, we introduce methods for the formal analysis of reachability and robustness of neural networks that are modeled as rational McNaughton functions by, first, stating such properties in the language of Łukasiewicz infinitely-valued logic and, then, using the (...) reasoning techniques of such logical system. We also present a case study where we employ the proposed techniques in an actual neural network that we trained to predict whether it will rain tomorrow in Australia. (shrink)

Kind representations, concepts like table, triangle, dog, and planet, underlie generic language. Here, we investigate the formal structure of kind representations—the structure that distinguishes kind representations from other types of representations. The present studies confirm that participants distinguish generic‐supporting properties of individuals (e.g., this watch is made of steel) and accidental properties (e.g., this watch is on the nightstand). Furthermore, work dating back to Aristotle establishes that only some generic‐supporting properties bear a principled connection to the (...) kind, that is, are true of an individual by virtue of its being a member of a specific kind (e.g., telling time for a watch). The present studies tested the hypothesis that principled connections are part of the formal structure of kind representations. Specifically, they tested whether they structure a newly learned kind representation. Experiment 1 found that introducing a property of a newly encountered novel kind in any one of four linguistic frames that provide evidence that a property has a principled connection to a kind (e.g., “It has fur because it is a blick”) led participants to infer a different conceptual consequence of principled connections (i.e., “There is something wrong with this blick, which does not have fur”) for which they had no direct evidence. Two introduction frames that provided no evidence for principled connections (e.g., “Almost all blicks have fur”) did not generate the same consequence. Experiment 2 found that all of the targeted properties were generic licensing, irrespective of the introduction frame. That the distinction between properties that bear principled connections to their kinds, and merely generic‐supporting properties structures novel kind representations, provides strong evidence that this distinction is part of the formal structure of kind representations. (shrink)

This paper describes an axiomatic theory BT, which is a suitable formal theory for developing constructive mathematics, due to its expressive language with countable number of set types and its constructive properties such as the existence and disjunction properties, and consistency with the formal Church thesis. BT has a predicative comprehension axiom and usual combinatorial operations. BT has intuitionistic logic and is consistent with classical logic. BT is mutually interpretable with a so called theory of arithmetical (...) truth PATr and with a second-order arithmetic SA that contains infinitely many sorts of sets of natural numbers. We compare BT with some standard second-order arithmetics and investigate the proof-theoretical strengths of fragments of BT, PATr and SA. (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)

This paper proposes a concept of creativity that stems from a semiotic and linguistic theoretical perspective, in which the formal frame of reference for variation and linguistic change considers and evaluates both the process of general interaction and the contact of languages as a global phenomenon. This method proposes an analysis of creativity that ranges from reflections of ancient philosophy to a contemporary linguistic perspective, incorporates international ideologies, and identifies, within the dimensions of use and social sharing, the (...) principle capable of guiding potentially unlimited forms of linguistic creativity that are self-expressive and communicative, far beyond the grammatical patterns of regularity and norm. Interpreting the paradigm of creativity according to this model means placing the semiotic property in a position of prima inter pares, entrusted not only with the “role” of forming signs (words, sentences, texts), but the function of arbitraire, as a phenomenon of language creation. The following reading references the semiotic contribution of Tullio De Mauro, an Italian linguist who has contributed to the systematization of creativity, overcoming and synthesizing both Saussurian structuralism and Chomskyan generativism. (shrink)

This paper explores the link between rules of grammar, grammar formalisms and the architecture of the language faculty. In doing so, it provides a flexible meta-level theory of the language faculty through the postulation of general axioms that govern the interaction of different components of grammar. The idea is simply that such an abstract formulation allows us to view the structure of the language faculty independently of specific theoretical frameworks/formalisms. It turns out that the system of rules, axioms and constraints (...) of grammar cannot beexplicitlyrepresented in a general architecture of the language faculty — which circumvents the ontological mismatch of mental representations and formal/axiomatic properties of language. Rather, the system of rules, axioms, constraints of grammar isintentionallyprojected by humans, and this projection realizes/instantiates what Dascal (1992) calls ‘psychopragmatics’. Relevant implications for linguistic theory, learnability and (computational) models of language processing are also explored. (shrink)

This book explores issues at the core of modern linguistics and cognitive science. Why are all languages similar in some ways and in others utterly different? Why do languages change and change variably? How did the human capacity for language evolve, and how far did it do so as an innate ability? Simon Kirby looks at these questions from a broad perspective, arguing that they can be studied together. The author begins by examining how far the universal (...) class='Hi'>properties of language may be explained by examining the way it is used, and how far by the way it is structured. He then considers what insights may be gained by combining functional and formal approaches. In doing so he develops a way of treating language as an adaptive system, in which its communicative and formal roles are both crucial and complementary. In order to test the effectiveness of competing theories and explanations, Simon Kirby develops computational models to show what universals emerge given a particular theory of language use or acquisition. He presents here both the methodology and the results. Function, Selection, and Innateness is important for its argument, its methodology, and its conclusions. It is a powerful demonstration of the value of looking at language as an adaptive system and goes to the heart of current debates on the evolution and nature of language. (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)

In this paper it is championed that a two stages hypothesis for the evolution of language must take into account a qualified approach to heterochrony and the available information from the archaeological record. As it seems, a protracted childhood and youth was already at work in Homo erectus, but early postnatal brain growth was only available to Homo sapiens. According to these facts, the term hysteron proteron is given here to the reversal that sets off linguistic capacity during the first (...) three years of life, upon the ancient abilities for social, natural and technological knowledge, which were already established during the last 2 Mya BP. The unfolding of linguistic capacity creates the typical effect that ontogeny reverses phylogeny: since late postnatal brain growth, quite recent in evolution, launches in ontogeny before the phylogenetically old processes of playing and learning take place during childhood and youth. Full symbolic abilities may be explained as emerging from older semiotic competences based on iconicity and indexicality, which would have presumably sustained human life for millennia. Furthermore, it is argued that the formation of linguistic categories follows from that overlaying of extended connectivity linked to early postnatal brain growth, inasmuch as it entangles and transforms previous iconic and referential information: i.e. the ancient semiotic capacities for proprioception, embodiment, extended mimesis and pragmatic knowledge, shaping a sort of self-organization process that provides the formal and semantic properties we find in articulated languages. (shrink)

This is a first attempt to formalize the language required for analysis of purposive organizations or systems into the subordinate systems of which they organically consist. The authors take a philosophic position midway between Atomism and the Absolute; like Aristotle, they take a finite, complex individual as the ultimate referent of explanation. The sole primitive is "s///tOx," interpreted as "upon analytic dissection, the system t organized by [the property] x." It is claimed without argument that the relationship is independent of (...) who, so to speak, is doing the dissecting. This paper is welcome as a first attack on a difficult problem, although it does not pay off in the production of non-trivial theorems or in clarification much beyond that afforded by technical English.--N. D. B. Jr. (shrink)

Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different such tools are being increasingly used in order to accelerate and simplify proof checking, and the Coq proof assistant is one of the most well known and used in large-scale projects. Language and automata theory is a well-established area of mathematics, relevant to computer science foundations and information technology. In particular, context-free language (...) theory is of fundamental importance in the analysis, design, and implementation of computer programming languages. This work describes a formalization effort, using the Coq proof assistant, of fundamental results of the classical theory of contextfree grammars and languages. These include closure properties (union, concatenation, and Kleene star), grammar simplification (elimination of useless symbols, inaccessible symbols, empty rules, and unit rules), the existence of a Chomsky Normal Form for context-free grammars and the Pumping Lemma for context-free languages. The result is an important set of libraries covering the main results of context-free language theory, with more than 500 lemmas and theorems fully proved and checked. As it turns out, this is a comprehensive formalization of the classical context-free language theory in the Coq proof assistant and includes the formalization of the Pumping Lemma for context-free languages. The perspectives for the further development of this work are diverse and can be grouped in three different areas: inclusion of new devices and results, code extraction, and general enhancements of its libraries. (shrink)

Some algebraic structures of the set of all effects are investigated and summarized in the notion of a(weak) orthoalgebra. It is shown that these structures can be embedded in a natural way in lattices, via the so-calledMacNeille completion. These structures serve as a model ofparaconsistent quantum logic, orthologic, andorthomodular quantum logic.

Abstract The purpose of this paper is twofold: (i) we will argue that formal semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of concepts, namely ontological concepts, that should be types in a strongly-typed ontology, and logical concepts, that are predicates corresponding to properties of, and relations between, objects of various ontological types; and (ii) we show that accounting for these differences amounts to a new formal semantics; one that (...) integrates lexical and compositional semantics in one coherent framework and one where formal semantics is embedded with a strongly typed ontology; an ontology that reflects our commonsense knowledge of the world and the way we talk about it in ordinary language. We will show how in such a framework a number of challenges in the semantics of natural language are adequately and systematically treated. (shrink)

Introduction. PHilosophy of Language and Linguistics: The Formal Turn Piotr Stalmaszczyk Gottlob Frege, Philosophy of Language, and Predication Piotr Stalmaszczyk Philosophy, Linguistics and Semantic Interpretation Christian Bassac An Unresolved Issue: Nonsense in Natural Language and Non-Classical Logical and Semantic Systems Elzbieta Chrzanowska-Kluczewska Varieties of Context-Dependence Tadeusz Ciecierski The Logos of Semantic Structure Marie Du í, Bjørn Jespersen and Pavel Materna The Good Samaritan and the Hygienic Cook: A Cautionary Tale About Linguistic Data Chris Fox The Meaning of Multiple Quantified (...) Sentences: Where Formal Semantics Meets Psycholinguistics Justyna Grudzinska The Hybrid Theory of Reference for Proper Names Filip Kawczynski On the Nature of Statistical Language Laws Agnieszka Kulacka Vagueness and Contextualism Joanna Odrowaz-Sypniewska The Myth of Semantic Structure Jaroslav Peregrin Scalar Implicatures, Communication and Language Evolution Salvatore Pistoia Reda Semantics and Contextuality: The Case of Pia s Leaves Stefano Predelli Is Logico-Semantical Analysis of Natural Language Expressions a Translation? Jirí Raclavský Beyond the Fregean Myth: The Value of Logical Values Fabien Schang Modal Calculus of Illocutionary Logic Andrew Schumann Subjectivity in Philosophy and Linguistics Barbara Sonnenhauser Asymmetrical Semantics Mieszko Talasiewicz Truth: An Anti-realist Adequacy Condition Luca Tranchini Belief Reports: Defaults, Intentions and Scorekeeping Giacomo Turbanti On Truth in Time Bartosz Wieckowski Order William J. SUllivan Indexes. (shrink)

The van Wijngaarden grammars are two-level grammars that present many interesting properties. In the present article I elaborate on six of these properties, to wit, (i) their being constituted by two grammars, (ii) their ability to generate (possibly infinitely many) strict languages and their own metalanguage, (iii) their context-sensitivity, (iv) their high descriptive power, (v) their productivity, or the ability to generate an infinite number of production rules, and (vi) their equivalence with the unrestricted, or Type-0, Chomsky (...) grammars. (shrink)

Natural language meaning has properties of both (embodied) cognitive representations and formal/mathematical structures. But it is not clear how they actually relate to one another. This article argues that how properties of cognitive representations and formal/mathematical structures of natural language meaning can be united remains one of the puzzles in cognitive science. That is primarily because formal/mathematical structures of natural language meaning are abstract, logical, and truth‐conditional properties, whereas cognitive/conceptual representations are embodied and grounded (...) in sensory‐motor systems. After reviewing the current progress, this work offers, in outline, the general formulations that show how these two different kinds of representations for semantic structures can (potentially) be unified and also proposes three desiderata for testing, in brain dynamics, the mathematical equivalence between formal symbolic representations (and their transitions), and neuronal population codes (and their transitions). (shrink)

The traditional view is that 'now’ is a pure indexical, denoting the utterance time. Yet, despite its initial appeal, the view has faced criticism. A range of data reveal 'now’ allows for discourse-bound (i.e., anaphoric) uses, and can occur felicitously with the past tense. The reaction to this has typically been to treat ‘now’ as akin to a true demonstrative, selecting the prominent time supplied by the non-linguistic context or prior discourse. We argue this is doubly mistaken. The first mistake (...) concerns the semantic value of ‘now’, which is not a time, but a state — the consequent state of a prominent event. The second is that ‘now’ is a pure indexical after all, insofar as its interpretation is determined without recourse to extra-linguistic supplementation. Specifically, we argue that any occurrence of 'now’ selects the consequent state of the most prominent event, where event-prominence is linguistically maintained through prominence-affecting updates contributed by coherence relations. Our analysis accounts straightforwardly for a wide range of discourse initial and discourse bound uses of ‘now’, while giving it a simple indexical meaning. (shrink)

The heuristics and strategies presented in Lakatos' Proofs and Refutations are well-known. However they hardly present the whole story as many authors have shown. In this paper a recent, rather spectacular, event in the history of mathematics is examined to gather evidence for two new strategies. The first heuristic concerns the expectations mathematicians have that a statement will be proved using given methods. The second heuristic tries to make sense of the mathematicians' notion of the quality of a proof.

This paper articulates a formal theory of belief incorporating three key theses: (1) belief is a dyadic relation between an agent and a property; (2) this property is not the belief's truth condition (i.e., the intuitively self-ascribed property which the agent must exemplify for the belief to be true) but is instead a certain abstract property (a "thought-content") which contains a way of thinking of that truth condition; (3) for an agent a to have a belief "about" such-and-such items (...) it is necessary that a possesses a language of thought, $M_{a}$ , and that a (is disposed as one who) inwardly affirms a sentence of $M_{a}$ in which there are terms that denote those objects. Employing an extended version of E. Zalta's system ILAO, the proffered theory locates thought-contents within a typed hierarchy of "senses" and their "modes of presentation", the provisional definitions of which (suppressing complications added later to accommodate the contents of beliefs about beliefs) are as follows. A mode of presentation of e is a ternary relation of the sort [λxyz z is a name in $M_{y}$ that denotes x, and $D_{e}yz$ ] in which $D_{e}$ is an e-determiner - a relation between agents and their mental expressions imposing a syntactico-semantic condition sufficient for such an expression to denote e therein. A sense of an entity e is an abstract property that "contains" a mode of presentation $R_{e}$ of e by dint of encoding its property-reduct [λx(∃y)(∃z) $R_{e}xyz$ ]. In particular, a thought-content is a sense T of an ordinary first-order property P containing a mode of presentation whose P-determiner $D_{P}$ is such that, for any y and z, $D_{P}yz$ entails that z is a λ-abstract [λv S] of $M_{y}$ in which S is a sentence whose non-logical parts stand in appropriate semantic relations to the constituents of T's (some of which may themselves be senses). Where $I_{a}$ is agent a's dedicated self-demonstrative and |T| is the mode of presentation contained in a thought-content T, the belief relation itself is then characterized as obtaining between a and T iff a( is disposed as one who) inwardly affirms the substitution instance $S(I_{a}/v)$ of a sentence S in $M_{a}$ such that |T|(P, a, [λv S]). The aforementioned "constituents" and "appropriate semantic relations" are formally characterized so as to permit a system of canonical descriptions for thought-contents of arbitrary complexity. These canonical descriptions are then employed to chart the nature and interrelations of belief de re, de dicto and de se and to identify the source of opacity in belief ascription. (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 previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate meta-language to speak of the proposed ontology of properties and its structure.

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results (...) hold for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics. (shrink)

Suppose you attend a seminar where a mathematician presents a proof to some of his colleagues. Suppose further that what he is proving is an important mathematical statement Now the following happens: as the mathematician proceeds, his audience is amazed at first, then becomes angry and finally ends up disturbing the lecture (some walk out, some laugh, …). If in addition, you see that the proof he is presenting is formally speaking (nearly) correct, would you say you are witnessing an (...) extraordinary event in urgent need of explanation? Surely, your answer would be yes. But do events of this type actually occur? The matter of the fact is, yes, they do. This paper presents the details of such an event, suggests a possible explanation and examines its implications for our understanding of mathematical practice. (shrink)

The essays in this collection are the outgrowth of a workshop, held in June 1976, on formal approaches to the semantics and pragmatics of natural languages. They document in an astoundingly uniform way the develop ments in the formal analysis of natural languages since the late sixties. The avowed aim of the' workshop was in fact to assess the progress made in the application of formal methods to semantics, to confront different approaches to essentially the (...) same problems on the one hand, and, on the other, to show the way in relating semantic and pragmatic explanations of linguistic phenomena. Several of these papers can in fact be regarded as attempts to close the 'semiotic circle' by bringing together the syntactic, semantic and pragmatic properties of certain constructions in an explanatory framework thereby making it more than obvious that these three components of an integrated linguistic theory cannot be as neatly separated as one would have liked to believe. In other words, not only can we not elaborate a syntactic description of (a fragment of) a language and then proceed to the semantics (as Montague pointed out already forcefully in 1968), we cannot hope to achieve an adequate integrated syntax and semantics without paying heed to the pragmatic aspects of the constructions involved. The behavior of polarity items, 'quantifiers' like any, conditionals or even logical particles like and and or in non-indicative sentences is clear-cut evidence for the need to let each component of the grammar inform the other. (shrink)