We address the impingement of Artificial Intelligence (AI) on logic, by examining the requirements posed on logic by knowledge representation and reasoning issues which A I has addressed. We then outline some of AI's contributions, via Logic Programming, to more dynamic forms of logic, in order to deal with knowledge in flux, namely: incomplete and contradictory information; hypotheses making through abduction; argumentation; diagnosis and debugging; updating; and learning. Along the way we delve into implications for the philosophy of knowledge.

We address the impingement of Artificial Intelligence (AI) on logic, by examining the requirements posed on logic by knowledge representation and reasoning issues which A I has addressed. We then outline some of AI's contributions, via Logic Programming, to more dynamic forms of logic, in order to deal with knowledge in flux, namely: incomplete and contradictory information; hypotheses making through abduction; argumentation; diagnosis and debugging; updating; and learning. Along the way we delve into implications for the philosophy of knowledge.

This book addresses the fundamentals of machine ethics. It discusses abilities required for ethical machine reasoning and the programming features that enable them. It connects ethics, psychological ethical processes, and machine implemented procedures. From a technical point of view, the book uses logic programming and evolutionary game theory to model and link the individual and collective moral realms. It also reports on the results of experiments performed using several model implementations. Opening specific and promising inroads into the terra incognita of (...) machine ethics, the authors define here new tools and describe a variety of program-tested moral applications and implemented systems. In addition, they provide alternative readings paths, allowing readers to best focus on their specific interests and to explore the concepts at different levels of detail. Mainly written for researchers in cognitive science, artificial intelligence, robotics, philosophy of technology and engineering of ethics, the book will also be of general interest to other academics, undergraduates in search of research topics, science journalists as well as science and society forums, legislators and military organizations concerned with machine ethics. (shrink)

In this essay we advance the view that analytical epistemology and artificial intelligence are complementary disciplines. Both fields study epistemic relations, but whereas artificial intelligence approaches this subject from the perspective of understanding formal and computational properties of frameworks purporting to model some epistemic relation or other, traditional epistemology approaches the subject from the perspective of understanding the properties of epistemic relations in terms of their conceptual properties. We argue that these two practices should not be conducted in isolation. We (...) illustrate this point by discussing how to represent a class of inference forms found in standard inferential statistics. This class of inference forms is interesting because its members share two properties that are common to epistemic relations, namely defeasibility and paraconsistency. Our modeling of standard inferential statistical arguments exploits results from both logical artificial intelligence and analytical epistemology. We remark how our approach to this modeling problem may be generalized to an interdisciplinary approach to the study of epistemic relation. (shrink)

This paper proposes a classification of economic models into three types: historical, axiomatic and conditional. Historical or empirical models utilize the historical-deductive method, and are generalizations from the economic regularities and tendencies that we find in the real world. Axiomatic models utilize the hypothetical-deductive method; they are syllogisms whose major premise is an axiom – a self-evident truth; they are appropriate for methodological sciences such as mathematics and econometrics. Conditional economic models are likewise syllogisms, but they are suitable for economics (...) because they make for clearer and more precise economic reasoning. The criterion of truth of the substantive sciences is the conformity with reality, of the methodological science, its internal consistency. When a school of economic thought adopts mainly axiomatic models, as is the case with neoclassical economics, it implicitly falls into contradiction because their best representatives believe in the conformity with reality criterion. (shrink)

Source: "This book addresses the fundamentals of machine ethics. It discusses abilities required for ethical machine reasoning and the programming features that enable them. It connects ethics, psychological ethical processes, and machine implemented procedures. From a technical point of view, the book uses logic programming and evolutionary game theory to model and link the individual and collective moral realms. It also reports on the results of experiments performed using several model implementations. Opening specific and promising inroads into the terra incognita (...) of machine ethics, the authors define here new tools and describe a variety of program-tested moral applications and implemented systems. In addition, they provide alternative readings paths, allowing readers to best focus on their specific interests and to explore the concepts at different levels of detail. Mainly written for researchers in cognitive science, artificial intelligence, robotics, philosophy of technology and engineering of ethics, the book will also be of general interest to other academics, undergraduates in search of research topics, science journalists as well as science and society forums, legislators and military organizations concerned with machine ethics.". (shrink)

Epistemic naturalism holds that the results or methodologies from the cognitive sciences are relevant to epistemology, and some have maintained that scientific methods are more compatible with externalist theories of justification than with internalist theories. But practically all discussions about naturalized epistemology are framed exclusively in terms of cognitive psychology, which is only one of the cognitive sciences. The question addressed in this essay is whether a commitment to naturalism really does favor externalism over internalism, and we offer reasons for (...) thinking that naturalism in epistemology is compatible with both internalist and externalist conceptions of justification. We also argue that there are some distinctively internalist aims that are currently being studied scientifically and these notions, and others, should be studied by scientific methods. (shrink)

ABSTRACT One major problem in the process of knowledge assimilation is how to deal with inconsistency of new knowledge and the existing knowledge base. In this paper we present a formal, provably correct and yet computational methodology for assimilation of new knowledge into knowledge bases about actions and changes based on the slogan: what is believed is what is explained. Technically, we employ Gelfond and Lifschitz' action description language A to describe domains of actions. The knowledge bases on domains of (...) actions are defined and obtained by a new translation from domain descriptions in A into abductive normal logic programs, where a time dimension is incorporated. The knowledge bases are shown to be both sound and complete with respect to their domain descriptions. In particular, we propose a possible causes approach (PCA) to knowledge assimilation about evolving domains of actions, in contrast to Ginsberg's possible worlds approach (PWA) and Winslett's possible models approach (PMA). A possible cause of new knowledge consists of abduced occurrences of actions and value propositions about the initial state of the domain of actions, that would allow to derive the new knowledge. We show how to compute possible causes with abductive logic programming, and present some techniques to improve search efficiency. We use examples to compare our possible causes approach with syntax-based approaches, such as Ginsberg's possible worlds approach, and semantics-based approaches, such as Winslett's possible models approach, to belief revision/update. (shrink)

In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kowalski. The importance of this result is that for the first time a framework encompassing several quite distinct logic programming semantics is described, namely Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic (...) Logic Programming. Moreover, the embedding provides a more general semantical structure paving the way for defining paraconsistent probabilistic reasoning with a logic programming semantics. (shrink)

The relation between ex falso and disjunctive syllogism, or even the justification of ex falso based on disjunctive syllogism, is an old topic in the history of logic. This old topic reappears in contemporary logic since the introduction of minimal logic by Johansson. The disjunctive syllogism seems to be part of our general non-problematic inferential practices and superficially it does not seem to be related to or to depend on our acceptance of the frequently disputable ex falso rule. We know (...) that the acceptance of the ex falso is a sufficient condition for the acceptance of the disjunctive syllogism, but the interesting question is: is the ex falso a necessary condition for the acceptance of the disjunctive syllogism? The aim of the present paper is to discuss some possible ways to define systems that combines the preservation of the disjunctive syllogism with the rejection of the ex falso. (shrink)

The impact of Cyberculture, of digital devices on young people as extensions of the body, can be seen in terms of the decreasing structuring of thoughts and information, increasing impulsivity in perception and action, and the development of more primitive defense mechanisms. These adverse impacts result in the feeling of isolation and devaluation, frustration of present and uncertainty of the future, exteriorization and floating identities, mimetic and adhesive identifications, less cohesion of the self, and decreasing tolerance of the other. This (...) paper focuses on the following themes: Symbiosis versus syncretism: The affirmations of symbiosis. The dilutions of syncretism. Synopsis: Too much syncretism, too little symbiosis. Lack of a deeper co-construction of knowledge, more lasting, and sustainable. Lack of increased more independent personal cognitive deepening. Lack of ability to be alone. Causality and free will: Symbiotic versus syncretic causality. Conclusions: Cyber-selfs—either distributed or not at all? (shrink)

Human beings have been aware of the risks associated with knowledge or its associated technologies since the dawn of time. Not just in Greek mythology, but in the founding myths of Judeo-Christian religions, there are signs and warnings against these dangers. Yet, such warnings and forebodings have never made as much sense as they do today. This stems from the emergence of machines capable of cognitive functions performed exclusively by humans until recently. Besides those technical problems associated with its design (...) and conceptualization, the cognitive revolution, brought about by the development of AI also gives rise to social and economic problems that directly impact humanity. Therefore, it is vital and urgent to examine AI from a moral point of view. The moral problems are two-fold: on the one hand, those associated with the type of society we wish to promote through automation, complexification and power of data processing available today; on the other, how to program decision-making machines according to moral principles acceptable to those humans who will share knowledge and action with them. (shrink)

In 2015 Dag Prawitz proposed an Ecumenical system where classical and intuitionistic logic could coexist in peace. The classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation and the constant for the absurd, but they would each have their own existential quantifier, disjunction and implication, with different meanings. Prawitz’ main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. The aim of the present paper is [1] (...) to prove the normalization theorem for the propositional fragment NEp of Prawitz’ ecumenical system, and [2] to show that NEp is sound and complete with respect to a Kripke-style semantics for the language of NEp. (shrink)

Proceedings of the Tenth Brazilian Conference on Mathematical Logic. Coleção CLE, volume 14, 1995. Centro De Lógica, Epistemologia e História da Ciência, Unicamp, Campinas, SP, Brazil.

Sambin [6] proved the normalization theorem for GL, the modal logic of provability, in a sequent calculus version called by him GLS. His proof does not take into account the concept of reduction, commonly used in normalization proofs. Bellini [1], on the other hand, gave a normalization proof for GL using reductions. Indeed, Sambin's proof is a decision procedure which builds cut-free proofs. In this work we formalize this procedure as a recursive function and prove its recursiveness in an arithmetically (...) formalizable way, concluding that the normalization of GL can be formalized in PA. MSC: 03F05, 03B35, 03B45. (shrink)

Sambin [6] proved the normalization theorem for GL, the modal logic of provability, in a sequent calculus version called by him GLS. His proof does not take into account the concept of reduction, commonly used in normalization proofs. Bellini [1], on the other hand, gave a normalization proof for GL using reductions. Indeed, Sambin's proof is a decision procedure which builds cut-free proofs. In this work we formalize this procedure as a recursive function and prove its recursiveness in an arithmetically (...) formalizable way, concluding that the normalization of GL can be formalized in PA. MSC: 03F05, 03B35, 03B45. (shrink)

In 1930, Johann von Neumann, together with Rudolf Carnap and Arend Heyting, participated in a conference held in Königsberg, called “Second Seminar on the Epistemology of Exact Sciences”. The idea behind the reunion of these three researchers was to compose a fairly faithful picture of the three main foundational programs of mathematics at the time: formalism, logicism, and intuitionism. The main objective of this paper is to propose an analysis of the text “The Formalist Foundation of Mathematics” presented by von (...) Neumann in this conference. We show how, from von Neumann's perspective, the problem of the consistency of mathematical theories results from the transformation of a genuinely philosophical question into a genuinely logical-mathematical question and how a proof of consistency could be seen as the solution to the foundational problem. In the final part of the text, we present some considerations about Gerhard Gentzen’s consistency proofs and their importance to contemporary proof theory. (shrink)

This paper deals with the recent Swedish proposals of a Intuitionistic notion of Truth, by Dag Prawitz and Per Martin-Löf.

The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce's formula → A) → A). E. Zimmermann [6] has shown how to extend Prawitz' normalization strategy to Peirce's rule: applications of Peirce's rule can be restricted to atomic conclusions. The aim of the present paper is to extend (...) Seldin's normalization strategy to Peirce's rule by showing that every derivation Π in the implicational fragment can be transformed into a derivation Π' such that no application of Peirce's rule in Π' occurs above applications of →-introduction and →-elimination. As a corollary of Seldin's normalization strategy we obtain a form of Glivenko's theorem for the classical {→}-fragment. (shrink)

Logic does not have purely existential theorems: the only existential sentences that are valid are those with valid universal analogues. Here, we show indeed this is so, when properly interpreted: every existential validity has a simple universal analogue, which is also valid. We also characterize existential and universal validities in terms of tautologies.

A natural extension of Natural Deduction was defined by Schroder-Heister where not only formulas but also rules could be used as hypotheses and hence discharged. It was shown that this extension allows the definition of higher-level introduction and elimination schemes and that the set $\{ \vee, \wedge, \rightarrow, \bot \}$ of intuitionist sentential operators forms a {\it complete} set of operators modulo the higher level introduction and elimination schemes, i.e., that any operator whose introduction and elimination rules are instances of (...) the higher-level schemes can be defined in terms of $\{ \vee, \wedge, \rightarrow, \bot \}$.The aim of the present work is to extend the well-known connections between Proof Theory and Category Theory to higher-level Natural Deduction. To be precise, we will show how an adjointness between cartesian closed categories with finite coproducts can be associated, in a systematic way, with any operator $\phi$ defined by the higher-level schemes. The objects in the categories will be rules instead of formulas. (shrink)

In 2015 Dag Prawitz proposed a natural deduction ecumenical system, where classical logic and intuitionistic logic are codified in the same system. In his ecumenical system, Prawitz recovers the harmony of rules, but the rules for the classical operators do not satisfy separability. In fact, the classical rules are not pure, in the sense that negation is used in the definition of the introduction and elimination rules for the classical operators. In this work we propose an ecumenical system adapting, to (...) the natural deduction framework, Girard’s mechanism of stoup. This allows for the definition of a pure harmonic natural deduction system for the propositional fragment of Prawitz’s ecumenical logic. We conclude by presenting an extension proposal to the first-order setting and a different approach to purity based on some ideas proposed by Julien Murzi. (shrink)

Veloso-Pereira-Haeusler_On-what-there-must-be.

Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {nEK}$$\end{document}, where exactly one logical operator figures (...) in introduction rules and every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic EK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {EK}$$\end{document}. We prove that nEK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {nEK}$$\end{document} is sound and complete w.r.t. the ecumenical birelational semantics and discuss fragments and extensions. (shrink)

Livro em homenagem ao filósofo brasileiro Luiz Henrique Lopes, um dos maiores expoentes da filosofia analítica. Neste livro grandes nomes da filosofia brasileira discorrem sobre a filosofia analítica e vários assuntos da filosofia contemporânea.

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science.

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order (...) rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism, via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction. (shrink)

RESUMO Na "Kritik der praktischen Vernunft", os conceitos do factum da razão e do sentimento de respeito pela lei moral geram grandes divergências interpretativas. O presente artigo tem como objetivo apresentar as interpretações de Zeljko Loparic, Guido Antônio de Almeida e Flávia Carvalho Chagas. ABSTRACT In "Kritik der praktischen Vernunft", the concepts of factum of reason and of feeling of respect for the moral law generate great interpretative divergences. This paper aims to present the interpretations of Zeljko Loparic, Guido Antônio (...) de Almeida and Flávia Carvalho Chagas. (shrink)