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Showing papers on "Paraconsistent logic published in 2004"


Book ChapterDOI
01 Jan 2004
TL;DR: The main aim of this paper is to review the measures of information and contradiction, and to study some potential practical applications, which have significant potential in developing intelligent systems that can be tolerant to inconsistencies when reasoning with real-world knowledge.
Abstract: Measures of quantity of information have been studied extensively for more than fifty years. The seminal work on information theory is by Shannon [67]. This work, based on probability theory, can be used in a logical setting when the worlds are the possible events. This work is also the basis of Lozinskii's work [48] for defining the quantity of information of a formula (or knowledgebase) in propositional logic. But this definition is not suitable when the knowledgebase is inconsistent. In this case, it has no classical model, so we have no “event” to count. This is a shortcoming since in practical applications (e.g. databases) it often happens that the knowledgebase is not consistent. And it is definitely not true that all inconsistent knowledgebases contain the same (null) amount of information, as given by the “classical information theory”. As explored for several years in the paraconsistent logic community, two inconsistent knowledgebases can lead to very different conclusions, showing that they do not convey the same information. There has been some recent interest in this issue, with some interesting proposals. Though a general approach for information theory in (possibly inconsistent) logical knowledgebases is missing. Another related measure is the measure of contradiction. It is usual in classical logic to use a binary measure of contradiction: a knowledgebase is either consistent or inconsistent. This dichotomy is obvious when the only deductive tool is classical inference, since inconsistent knowledgebases are of no use. But there are now a number of logics developed to draw non-trivial conclusions from an inconsistent knowledgebase. So this dichotomy is not sufficient to describe the amount of contradiction of a knowledgebase, one needs more fine-grained measures. Some interesting proposals have been made for this. The main aim of this paper is to review the measures of information and contradiction, and to study some potential practical applications. This has significant potential in developing intelligent systems that can be tolerant to inconsistencies when reasoning with real-world knowledge.

138 citations


BookDOI
01 Jan 2004
TL;DR: This chapter discusses Logic, Epistemology and the Unity of Science: An Encyclopedic Project in the Spirit of Neurath and Diderot Shahid Rahman and John Symons, and some of the contributions from Non-Classical Logics.
Abstract: I. Some Programmatic Comments. 1. Logic, Epistemology and the Unity of Science: An Encyclopedic Project in the Spirit of Neurath and Diderot Shahid Rahman and John Symons. 2. An International Encyclopedia of the Unified Sciences translated by John Symons and Ramon Alvarado) Otto Neurath. II. Game Theory and Independence Friendly Logic as a Unifying Framework. 3. Towards a Unity of the Human Behavioral Sciences Herbert Gintis. 4. Some Coloured Remarks on the Foundations of Mathematics in the 20th Century Gerhard Heinzmann. 5. Logical Versus Nonlogical Concepts: An Untenable Dualism? Jaakko Hintikka. 6. Semantic Games in Logic and Epistemology Ahti-Veikko Pietarinen. 7. IF Logic, Game-Theoretical Semantics and New Prospects for Philosophy of Science Ahti-Veikko Pietarinen and Gabriel Sandu. III. Unity and Plurality in Science and in Logic. 8. Concepts Structured through Reduction: A Structuralist Resource Illuminates the Consolidation-Long-Term Potentiation (LTP) Link John Bickle. 9. The Unity of Science and the Unity of Being: A Sketch of a Formal Approach C. Ulises Moulines. 10. Logical Pluralism and the Preservation of Warrant Greg Restall. 11. In Defence of the Dog: Response to Restall Stephen Read. 12. Normic Laws, Non-monotonic Reasoning, and the Unity of Science Gerhard Schurz. 13. The Puzzling Role of Philosophy in Life Sciences: Bases for a Joint Program for Philosophy and History of Science Juan Manuel Torres. 14. The Creative Growth of Mathematics Jean Paul Van Bendegem. 15. Quantum Logic and the Unity of Science John Woods and Kent Peacock. IV. The Logic of the Knowledge-Seeking Activities. 16. Belief Contraction, Anti-formulae and Resource Overdraft: Part II Deletion in Resource Unbounded Logics Dov Gabbay, Odinaldo Rodrigues and John Woods. 17. Reasoning about Knowledge in Linear Logic: Modalities and Complexity Mathieu Marion and Mehrnouche Sadrzadeh. 18. A Solution to Fitch's Paradox of Knowability Helge Ruckert. 19. Theories of Knowledge and Ignorance Wiebe van der Hoek, Jan Jaspars and Elias Thijsse. 20. Action-Theoretic Aspects of Theory Choice Heinrich Wansing. 21. Some Computational Constraints in Epistemic Logic Timothy Williamson. IV. Contributions from Non-Classical Logics. 22. The Need for Adaptive Logics in Epistemology Diderik Batens. 23. Logics for Qualitative Reasoning Paulo Veloso and Walter Carnielli. 24. Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples Bob Coecke, David J. Moore and Sonja Smets. 25. Complementarity and Paraconsistency Newton C. A. Da Costa and Decio Krause. 26. Law, Logic, Rhetoric: a Procedural Model of Legal Argumentation Arno Lodder. 27. Essentialist Metaphysics in a Scientific Framework Ulrich Nortmann. Index.

137 citations


Journal ArticleDOI
TL;DR: New logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic are introduced and form part of a much larger family of similar logics.
Abstract: This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning.

116 citations


Journal ArticleDOI
TL;DR: A paraconsistent reasoning strategy, Chunk and Permeate, where information is broken up into chunks, and a limited amount of information is allowed to flow between chunks to establish the legitimacy of reasoning of this kind.
Abstract: In this paper we introduce a paraconsistent reasoning strategy, Chunk and Permeate In this, information is broken up into chunks, and a limited amount of information is allowed to flow between chunks We start by giving an abstract characterisation of the strategy It is then applied to model the reasoning employed in the original infinitesimal calculus The paper next establishes some results concerning the legitimacy of reasoning of this kind – specifically concerning the preservation of the consistency of each chunk – and concludes with some other possible applications and technical questions

78 citations


Journal Article
TL;DR: In this article, the most natural predicative extension of Schutte's maximally paraconsistent logic, CLuNs, was devised and studied, and the system itself raised several interesting questions.
Abstract: In the present paper we devise and study the most natural predicative extension of Schutte’s maximally paraconsistent logic. With some of its large fragments, this logic, CLuNs, forms the most popular family of paraconsistent logics. Devising the system involves some entanglements, and the system itself raises several interesting questions. As the system and fragments were studied by other authors, we restrict our attention to results that we have not seen in press.

56 citations


Journal ArticleDOI
TL;DR: The representation of N4-lattices is obtained showing that the structure of an arbitrary N4, the paraconsistent variant of Nelson's logic with strong negation is completely determined by a suitable implicative lattice with distinguished filter and ideal.
Abstract: N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. Finally, subdirectly irreducible N4-lattices are described.

54 citations


Proceedings ArticleDOI
19 Jul 2004
TL;DR: This paper addresses ourselves to formalize an expressive logic of argumentation, called a Logic of Multiple-valued Argumentation (LMA), on top of the very expressive knowledge representation language, called Extended Annotated Logic Programming (EALP).
Abstract: This paper provides a new departure from the traditional two-valued argumentation frameworks. We address ourselves to formalize an expressive logic of argumentation, called a Logic of Multiple-valued Argumentation (LMA), on top of the very expressive knowledge representation language, called Extended Annotated Logic Programming (EALP), and examine its logical properties in various ways. EALP allows us to represent different kinds of uncertainty such as vagueness and inconsistency (or paraconsistency) in terms of multi-valuedness, and incompleteness with the help of default negation. LMA is a full-dress logic of argumentation in which agents can argue with other contenders, using multiple-valued knowledge base in terms of EALP.

46 citations


Journal ArticleDOI
Diderik Batens1
TL;DR: It is shown that the (flat) consequence relations defined from the Rescher-Manor Mechanism are all inconsistency-adaptive logics combined with a specific interpretation schema for the premises.
Abstract: It is shown that the (flat) consequence relations defined from the Rescher-Manor Mechanism (that is: in terms of maximal consistent subsets of the premises) are all inconsistency-adaptive logics combined with a specific interpretation schema for the premises. Each of the adaptive logics is obtained by applying a suitable adaptive strategy to the paraconsistent logic CLuN. This result provides all those consequence relations with a (dynamic) proof theory and with a static (as well as a dynamic) semantics.

46 citations


Journal ArticleDOI
TL;DR: This paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part of classical prepositional calculus and may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.
Abstract: For the given logical calculus we investigate the proportion of the number of true formulas of a certain length n to the number of all formulas of such length. We are especially interested in asymptotic behavior of this fraction when n tends to infinity. If the limit exists it is represented by a real number between 0 and 1 which we may call the density of truth for the investigated logic. In this paper we apply this approach to the intuitionistic logic of one variable with implication and negation. The result is obtained by reducing the problem to the same one of Dummett's intermediate linear logic of one variable (see [2]). Actually, this paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part (more than 93%) of classical prepositional calculus. Despite using strictly mathematical means to solve all discussed problems, this paper in fact, may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.

37 citations


Book ChapterDOI
01 Jan 2004
TL;DR: The authors argued that rational debate over the Law of Non-Contradiction can be carried out without a minimal set of logical resources without which rational debate is impossible, and argued that this response is misguided.
Abstract: A common response to those who question the Law of Non-Contradiction (LNC) is that it is impossible to debate such a fundamental law of logic. The reasons for this response vary, but what seems to underlie them is the thought that there is a minimal set of logical resources without which rational debate is impossible. This chapter argues that this response is misguided. First, it defends non-apriorism in logic: the view that logic is in the same epistemic boat as other scientific theories. It then offers an account of logical theory change in terms of this epistemology. The LNC is discussed in terms of this account of logical theory change, and it is shown that rational debate over this law can, and does, proceed. Finally, arguments for and against the LNC are discussed, and how and where non-a priori considerations arise in these arguments are illustrated.

35 citations


Book
01 Jan 2004
TL;DR: The authors The Mathematical Turn in Logic: From General to Transcendental Logic (M. Tiles) is a seminal work in the history of logic, with a focus on algebraic logic.
Abstract: Preface (D.M. Gabbay, J. Woods). List of Contributors. Leibniz's Logic (W. Lenzen). Kant: From General to Transcendental Logic (M. Tiles). Hegel's Logic (J.W. Burbidge). Bolzano as Logician (P. Rusnock, R. George). Husserl's Logic (R. Tieszen). Algebraical Logic 1685-1900 (T. Hailperin). The Algebra of Logic (V.S. Valencia). The Mathematical Turn in Logic (I. Grattan-Guinness). Schroder's Logic (V. Peckhaus). Peirce's Logic (R. Hilpinen). Frege's Logic (P. Sullivan). Index.

Journal Article
TL;DR: This paper proposes a granular logic that defines the G -formula, G -clause and G -literal, and to give the methods of G -resolution in the logic, and the soundness and completeness of the theorem for G - Resolution refutation are discussed.
Abstract: This paper proposes a granular logic, in brief written by G -logic, constructs the systems of approximate reasoning in the G -logic. It defines the G -formula, G -clause and G -literal, and to give the methods of G -resolution in the logic. The soundness theorem of the G -resolution is also proved. The logical formulas are an ordered binary pair, the first element is an assertion and the second is a definable domain or approximations of undefinable domain corresponding to the assertion. The logic is defined on information system IS=(U,A). So the assignment to individual variables in the formulas is an entity on U. The propositions or predicates in the formula are interpreted as attributes in A, hence meaning set of proposition or predicate is a subset on U, the pair of constructed by attribute and its meaning set together is called as an elementary granule. And the elementary granules are used as G -atoms in the logic. A G -formula in the logic is combined by the G -atoms with granular logical connectives. Satisfibility of the logical formula is that meaning set corresponding to it is not empty. If the domain of a formula in the logic is undefinable then the formula is discussed in the rough lower and upper approximations of the domain. The study of G -logic opens a new path for applications of classical logic. G -logic provides a better theoretical tool for treating of irregular knowledge. The operation of G -logic involves the decomposing of global and amalgamating of locals, thus it provides a new idea for solving -problem in AI. G -logic is a new generalization of Rough Logic, truth concept and its operations of the logic is different from classical logic and all non -standard logic. The logic is both logic and set theory. Thus it may use the logical methods when treating truth values and its operations, and it may also avoid the calculation of literal unifier with set theory approach in the G -resolution. Finally, the validity and feasibility of the G -resolution are illustrated with real examples. The related theorems in machine theorem proving are proposed and the soundness and completeness of the theorem for G -resolution refutation are discussed.

Book ChapterDOI
01 Jan 2004
TL;DR: It is shown how certain paraconsistent reasoning principles can be naturally formulated or reformulated by means of quantified Boolean formulas, and polynomial-time constructible encodings providing axiomatisations of the given reasoning tasks are described.
Abstract: Quantified propositional logic is an extension of classical propositional logic where quantifications over atomic formulas are permitted. As such, quantified propositional logic is a fragment of second-order logic, and its sentences are usually referred to as quantified Boolean formulas (QBFs). The motivation to study quantified propositional logic for paraconsistent reasoning is based on two fundamental observations. Firstly, in recent years, practicably efficient solvers for quantified propositional logic have been presented. Secondly, complexity results imply that there is a wide range of paraconsistent reasoning problems which can be efficiently represented in terms of QBFs. Hence, solvers for QBFs can be used as a core engine in systems prototypically implementing several of such reasoning tasks, most of them lacking concrete realisations. To this end, we show how certain paraconsistent reasoning principles can be naturally formulated or reformulated by means of quantified Boolean formulas. More precisely, we describe polynomial-time constructible encodings providing axiomatisations of the given reasoning tasks. In this way, a whole variety of a priori distinct approaches to paraconsistent reasoning become comparable in a uniform setting.

Book ChapterDOI
01 Jan 2004
TL;DR: The logic fde of first degree entailments is shown to arise naturally out of the deeper concerns of relevant logic, and especially the disjunctive syllogism is examined.
Abstract: This is an account of the approach to paraconsistency associated with relevant logic. The logic fde of first degree entailments is shown to arise naturally out of the deeper concerns of relevant logic. The relationship between relevant logic and resolution, and especially the disjunctive syllogism, is then examined. The relevant refusal to validate these inferences is defended, and finally it is suggested that more needs to be done towards a satisfactory theory of when they may nonetheless safely be used.

Book ChapterDOI
21 Oct 2004
TL;DR: In this article, the authors attempt to clarify the different readings of the law of non-contradiction, in particular taking cues from the tradition of relevant logics, and a further guiding principle will be the natural duality between the Law of Non-Contradiction and rejection on the one hand and the law on the excluded middle and acceptance on the other.
Abstract: There is widespread acknowledgement that the law of non-contradiction is an important logical principle. However, there is less-than-universal agreement on exactly what the law amounts to. This unclarity is brought to light by the emergence of paraconsistent logics in which contradictions are tolerated: From the point of view of proofs, not everything need follow from a contradiction — from the point of view of models, there are “worlds” in which contradictions are true. In this sense, the law of non-contradiction is violated in these logics. However, in many paraconsistent logics, statement (it is not the case that and not) is still provable. In this sense, the law of non-contradiction is upheld. This paper attempts to clarify the different readings of the law of non-contradiction, in particular taking cues from the tradition of relevant logics. A further guiding principle will be the natural duality between the law of non-contradiction and rejection on the one hand and the law of the excluded middle and acceptance on the

Journal ArticleDOI
TL;DR: In this article, the authors continue the investigation of paraconsistent extensions of minimal logic Lj started in [6, 7] and use the name "logic of classical refutability" to denote the logic Le obtained from Lj.
Abstract: This article continues the investigation of paraconsistent extensions of minimal logic Lj started in [6, 7]. The name “logic of classical refutability” is taken from the H.Curry monograph [1], where it denotes the logic Le obtained from Lj by adding the Peirce law.

Journal ArticleDOI
TL;DR: A system of analytic, paraconsistent and quasi-classical propositional logic that does not validate the paradoxes of Parry’s analytic implication is introduced.
Abstract: William Parry conceived in the early thirties a theory of entailment, the theory of analytic implication, intended to give a formal expression to the idea that the content of the conclusion of a valid argument must be included in the content of its premises. This paper introduces a system of analytic, paraconsistent and quasi-classical propositional logic that does not validate the paradoxes of Parry’s analytic implication. The interpretation of the expressions of this logic will be given in terms of a four-valued semantics, and its proof theory will be provided by a system of signed semantic tableaux that incorporates the techniques developed to improve the efficiency of the tableaux method for many-valued logics.

Journal ArticleDOI
TL;DR: A technique for measuring the degree of (in)coherence of inconsistent sets of propositional formulas is introduced, and Hunter's objections to many-valued paraconsistent logics as instruments for measuring (in]coherence are addressed.

BookDOI
01 Jan 2004
TL;DR: The Quantum Logic of Observables (QLOI) as discussed by the authors is a quantum logic from Quantum Computation (QC) that is based on Quantum Logic and Quantum Probability (QLP).
Abstract: I General Topics.- Why Is It Logical to Admit Several Logics?.- Does Metaphysics Need a Non-Classical Logic?.- Logic and the Philosophical Interpretation of Science.- How Set Theory Impinges on Logic.- Geometries and Arithmetics.- Remarks on Criteria of Truth and Models in Science.- Significant? Not Significant? The Dilemma of Statistical Induction in Scientific Research.- II Alternative Proposals.- Outline of a Paraconsistent Category Theory.- Combinatory Logic, Language, and Cognitive Representations.- Extending the Realm of Logic: The Adaptive-Logic Programme.- Comments on Jaakko Hintikka's Post-Tarskian Truth.- III Alternative Logics Motivated by Problems of Application to Science.- Applied Logics for Computer Science.- Stochastic versus Deterministic Features in Learning Models.- Praxic Logics.- Reasons from Science for Limiting Classical Logic.- The Language of Interpretation in Quantum Physics and Its Logic.- Why Objectivist Programs in Quantum Theory Do Not Need an Alternative Logic.- Does Quantum Physics Require a New Logic?.- Experimental Approach to Quantum-Logical Connectives.- From Semantics to Syntax: Quantum Logic of Observables.- An Unsharp Quantum Logic from Quantum Computation.- Quantum Logic and Quantum Probability.- Operator Algebras and Quantum Logic.

Journal ArticleDOI
01 Feb 2004
TL;DR: This paper presents an approach to approximate reasoning over a set of IF-THEN rules called fuzzy logic deduction, which understands IF- THEN rules as linguistically expressed logical implications and interprets them inside formal logical theory.
Abstract: This paper presents an approach to approximate reasoning over a set of IF-THEN rules called fuzzy logic deduction. It understands IF-THEN rules as linguistically expressed logical implications and interprets them inside formal logical theory. Methodology and some properties are presented.

Proceedings Article
22 Aug 2004
TL;DR: This work introduces a frame-based semantics of paraconsistent answer sets for extended disjunctive logic programs as a fully declarative approach, using Frames as a powerful and elegant tool to characterise and study substructural logics.
Abstract: In this work, paraconsistent answer sets for extended disjunctive logic programs are presented as a fully declarative approach. In order to do so, we introduce a frame-based semantics. Frames are a powerful and elegant tool which have been used to characterise and study substructural logics. Unlike the original definition, no kind of syntactic transformation is employed. Indeed, paraconsistent answer sets are defined by minimising models satisfying some conditions. Considering that paraconsistent answer sets embed both answer sets and stable models, these semantics are also captured via frames.

Journal ArticleDOI
TL;DR: A survey of three-valued paraconsistent propositional logics connected with Jaśkowski's criterion for constructing Paraconsistent Logics can be found in this paper, where several problems are raised and four new matrix 3-valued logics are suggested.
Abstract: A survey is given of three-valued paraconsistent propositional logics connected with Jaśkowski’s criterion for constructing paraconsistent logics. Several problems are raised and four new matrix three-valued paraconsistent logics are suggested.

Posted Content
TL;DR: This work considers the theoretical model of a quantum computer on a non commutative space background, which is a computational model for quantum gravity, and shows that a theorem that classically was considered true but non computable, at the Planck scale becomes computable but non decidable.
Abstract: We consider the issue of computability at the most fundamental level of physical reality: the Planck scale. To this aim, we consider the theoretical model of a quantum computer on a non commutative space background, which is a computational model for quantum gravity. In this domain, all computable functions are the laws of physics in their most primordial form, and non computable mathematics finds no room in the physical world. Moreover, we show that a theorem that classically was considered true but non computable, at the Planck scale becomes computable but non decidable. This fact is due to the change of logic for observers in a quantum-computing universe: from standard quantum logic and classical logic, to paraconsistent logic.

Book ChapterDOI
Joke Meheus1
01 Jan 2004
TL;DR: In this paper, the distinction between induction and deduction is less clear-cut than traditionally assumed, and moreover, most reasoning processes in the sciences involve an integration of inductive and deductive steps.
Abstract: The aim of this paper is twofold. First, I want to argue that the distinction between induction and deduction is less clear-cut than traditionally assumed, and that, moreover, most reasoning processes in the sciences involve an integration of inductive and deductive steps. Next, I want to show how so-called adaptive logics may lead to a better understanding of this integrated use of induction and deduction.

Posted Content
TL;DR: This work considers the logical assertions of a hypothetical observer who is inside a quantum computer and performs a reversible quantum measurement, obtaining a symmetric couple of new axioms, valid only inside the quantum computer.
Abstract: We consider the logical assertions of a hypothetical observer who is inside a quantum computer and performs a reversible quantum measurement, obtaining a symmetric couple of new axioms, valid only inside the quantum computer. The result is that, in this logical framework, symmetry and paraconsistency hold.

Journal ArticleDOI
TL;DR: This paper studies the relationship among classical logic, intuitionistic logic, and quantum logic (orthologic and orthomodular logic) through a dual intuitionistic Logic (a kind of paraconsistent logic).
Abstract: In this paper, we study the relationship among classical logic, intuitionistic logic, and quantum logic (orthologic and orthomodular logic). These logics are related in an interesting way and are not far apart from each other, as is widely believed. The results in this paper show how they are related with each other through a dual intuitionistic logic (a kind of paraconsistent logic). Our study is completely syntactical.

Book ChapterDOI
20 Sep 2004
TL;DR: This paper introduces how to apply EVALPSN to discrete event control with taking an example called Cat and Mouse, and shows that such a discrete event controlled by a paraconsistent logic program can be easily formalized in EVsN and implemented.
Abstract: We have developed a paraconsistent logic program called an Extended Vector Annotated Logic Program with Strong Negation (abbr. EVALPSN), which can deal with defeasible deontic reasoning and contradiction, and applied it to safety verification and control such as railway interlocking safety verification, traffic signal control etc.. In this paper, we introduce how to apply EVALPSN to discrete event control with taking an example called Cat and Mouse. Generally, event control can be represented as deontic rules such as it is forbidden for both the cat and the mouse to occupy the same room simultaneously, and the control must deal with contradiction to avoid unexpected system states. We show that such a discrete event control can be easily formalized in EVALPSN and implemented.

Book ChapterDOI
01 Jan 2004
TL;DR: In this paper, a broadening of the scope of symbolic logic is discussed, and the central idea concerns dynamic proofs that explicate forms of reasoning for which no positive test is available.
Abstract: This paper reports on a development that involves a drastic broadening of the scope of symbolic logic. The central idea concerns dynamic proofs that explicate forms of reasoning for which no positive test is available. Two other forms of the dynamics of reasoning are briefly spelled out.

Journal ArticleDOI
TL;DR: In this article, Nelson's constructive logics with strong negation have been viewed as alternative paraconsistent logic, and some philosophical aspects of Nelson's logics have been discussed.
Abstract: . David Nelson’s constructive logics with strong negation may be viewed as alternative paraconsistent logic. These logics have been developed before da Costa’s works. We address some philosophical aspects of Nelson’s logics and give technical results concerning Kripke models and tableau calculi. We also suggest possible applications of paraconsistent constructive logics.

Book ChapterDOI
08 Aug 2004
TL;DR: This paper proposes an argumentation framework with the paraconsistent logic programming based on the tetralemma, which allows it to represent typical eastern modes of truth: $\top, \bot$ which are considered epistemic states of propositions.
Abstract: Argumentation is a ubiquitous but effective mode of interaction and dialogue in the human society. It has come to be known that argumentation has many implications to interaction among computational agents as well. After observing and discussing the tetralemma, which is said to characterize the Eastern thought, in this paper we propose an argumentation framework with the paraconsistent logic programming based on the tetralemma. It allows us to represent typical eastern modes of truth: $\top, \bot$ which are considered epistemic states of propositions. We introduce various notions for our argumentation framework, such as attack relations in terms of differences as a momentum of argumentation, argument justification, preferential criteria of arguments based on social norms, and so on, in a way proper to the four-valued paraconsistent logic programming. Finally, we provide the fixpoint semantics and dialectical proof theory for the argumentation framework. We illustrate our ideas with various argument examples.