Showing papers on "Paraconsistent logic published in 1996"

The principles of mathematics revisited

Abstract: 1. The functions of logic and the problem of truth definition 2. The game of logic 3. Frege's fallacy foiled: Independence-friendly logic 4. The joys of independence: Some uses of IF logic 5. The complexities of completeness 6. Who's afraid of Alfred Tarski? Truth-definitions for IF first-order languages 7. The liar belied: negation in IF logic 8. Axiomatic set theory: Frankenstein's monster? 9. IF logic as a framework for mathematical theorizing 10. Constructivism reconstructed 11. The epistemology of mathematical objects.

Reasoning with logical bilattices

Abstract: The notion of bilattice was introduced by Ginsberg, and further examined by Fitting, as a general framework for many applications. In the present paper we develop proof systems, which correspond to bilattices in an essential way. For this goal we introduce the notion of logical bilattices. We also show how they can be used for efficient inferences from possibly inconsistent data. For this we incorporate certain ideas of Kifer and Lozinskii, which happen to suit well the context of our work. The outcome are paraconsistent logics with a lot of desirable properties. A preliminary version of this paper appears in Arieli and Avron (1994).

Combining Classical and Intuitionistic Logic

Abstract: We study how a logic C+J conbining classical logic C and intuitionistic logic J can be defined. We show that its Hilbert axiomatization cannot be attained by simply extending the union of the axiomatizations of C and J by so called interaction axioms. Such a logic would collapse into classical logic.

Malinowski and Suszko on many-valued logics: on the reduction of many-valuedness to two-valuedness

Abstract: We first describe the main features of Malinowski's book Many-Valued Logics: its orientation and its contents. The rest of our paper is devoted to the discussion of its original point, the presentation of Suszko's thesis, and questions directly related to it: What is many-valuedness? Are there only two truth-values? We analyse and discuss the characterization of many-valuedness and the reduction of many-valuedness to two-valuedness presented by Malinowski. Then we argue against Suszko's thesis, taking examples of paraconsistent logic and of Malinowski's inferential many-valuedness. However, we also present some arguments to reject supplementary truth-values in the case of two topics discussed by Malinowski: modality and partiality.

Evidential bilattice logic and lexical inference

Abstract: This paper presents an information-based logic that is applied to the analysis of entailment, implicature and presupposition in natural language. The logic is very fine-grained and is able to make distinctions that are outside the scope of classical logic. It is independently motivated by certain properties of natural human reasoning, namely partiality, paraconsistency, relevance, and defeasibility: once these are accounted for, the data on implicature and presupposition comes quite naturally.

Computing the well-founded model of deductive databases

Abstract: The well-founded model is one of the most popular models of general logic programs, i.e. logic programs with negation in the bodies of clauses. We present a method for constructing this model for general deductive databases, which are logic programs without any function symbols. The method adopts paraconsistent relations as the semantic objects associated with the predicate symbols of the database. Paraconsistent relations are a generalization of ordinary relations in that they allow manipulation of incomplete as well as inconsistent information. The first step in the model construction method is to transform the database clauses into paraconsistent relation definitions involving these operators. The second step is to build the well-founded model iteratively. Algorithms for both steps are presented and their termination and correctness is also established.

A case study in logical deconstruction: Formalizing J.D. Thompson's Organizations in Action in a multi-agent action logic

Abstract: Logic is a popular word in the social sciences, but it is rarely used as a formal tool. In the past, the logical formalisms were cumbersome and difficult to apply to domains of purposeful action. Recent years, however, have seen the advance of new logics specially designed for representing actions. We present such a logic and apply it to a classical organization theory, J.D. Thompson's Organizations in Action. The working hypothesis is that formal logic draws attention to some finer points in the logical structure of a theory, points that are easily neglected in the discursive reasoning typical for the social sciences. Examining Organizations in Action we find various problems in its logical structure that should, and, as we argue, could be addressed.

Consistency, Paraconsistency and Truth: Logic, the Whole Logic and Nothing but 'the' Logic

Abstract: After examining some components of a framework articulated in terms of general remarks on logic (in which two inadequate views of it are critically investigated), we present some arguments to the effect that a fallibilist, pluralist, though certainly not relativist, proposal might be interestingly pursued. Based on this proposal, we argue for a comprehensive agnosticism in connection to some issues raised by paraconsistency (in particular with regard to the existence of true contradictions). Such an agnosticism, not being phiiosophically committed to any particular "interpretative" claims surrounding paraconsistency, seems to be at the moment more adequate than the alternative proposals.

A Simple Signed System for Paraconsistent Reasoning

Abstract: We present a novel approach to paraconsistent reasoning, that is to reasoning from inconsistent information. The basic idea is the following. We transform an inconsistent theory into a consistent one by renaming all literals occuring in the theory. Then, we restore some of the original contents of the theory by introducing progressively formal equivalences linking the original literals to their renamings. This is done as long as consistency is preserved. The restoration of the original contents of the theory is done by appeal to default logic. The overall approach provides us with a family of paraconsistent consequence relations.

Dialectic operator fuzzy logic

Abstract: Dialectic operator fuzzy logic (DOFL) is presented which is relevant,paraconsistent and nonmonotonic.DOFL can vividly describe the belief revision in the cognitive process and can infer reasonably well while the knowledge is inconsistent,imprecise or incomplete.

Super Logic Programs and Negation as Belief

Abstract: the proposed syntax of such programs is sufficiently general to include the class of normal logic programs; the proposed syntax o] queries about such programs is sufficiently expressive to include the class of s tandard queries about normal logic programs; the proposed semantics of such programs is sufficiently powerful to precisely determine answers to the above queries and the answers, when restricted to normal logic programs, coincide with those provided by one of the wellestablished semantics of normal logic programs.

Philosophical logic and logical philosophy : essays in honour of Vladimir A. Smirnov

Abstract: Preface. Part I: Epistemology and Philosophy of Science. 1. Understanding Scientific Change V. Rantala. 2. Genetically-Constructive Ways of Theory Building V.S. Stiopin. 3. Toward Holistic Conception of Artificial Intelligence V.N. Sadovsky. Part II: Modern Logic and Methodology of Science. 4. Hierarchical Learning of Boolean Functions P. Suppes, S. Takahashi. 5. Inference, Methodology and Semantics J. van Benthem. 6. Theories in Science R. Wojcicki. 7. Structures, Suppes Predicates and Boolean-Valued Models in Physics N.C.A. da Costa, F.A. Doria. Part III: Logical Semantics. 8. World Lines and Their Role in Epistemic Logic J. Hintikka. 9. In Defence of Classical Principles I. Ruzsa. 10. The Semantics of 'All A's are B's' J.M. Moravcsik. Part IV: Non-Classical Logics. 11. Conditional Intentions I. Niiniluoto. 12. On Epistemic Modal Predicate Logic M.N. Bezhanishvili. 13. Normative Reasonings and Default Assumptions I. Gerasimova. 14. A Logic Without Fixed Points A.S. Karpenko. Part V: Analysis of Logical Proofs. 15. An Extension of Gentzen's Analysis of Logical Deduction to Second-Order Logic O.F. Serebriannikov. 16. The Sequent Variant of System R V.M. Popov. 17. Non-Standard Sequent Calculi for Modal and Relevant Logics P. Bystrov. 18. Axiomatic Rejection for Classical Propositional Logic A. Ishimoto. Selected Bibliography of Vladimir Aleksandrovich Smirnov's Works.

Paraconsistent circumscription: preliminary report

Abstract: In this paper we describe the paraconsistent circumscription by the application of predicate circumscription in a paraconsistent logic, the logic of paradox LP. In addition to circumscribing the predicates, we also circumscribe the inconsistency. The paraconsistent circumscription can be well characterized by the minimal semantics which is both nonmonotonic and paraconsistent. It brings us advantages in two respects: nonmonotonic logic would be nontrivial while there was a contradiction, and paraconsistent logic would be equivalent to classical logic while there was no effect of a contradiction.