Topic
Paraconsistent logic
About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.
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01 Jan 2007
TL;DR: A general Correspondence Theorem is stated showing that behind each epistemic modal logic, there is a robust system of justifications, which renders a new, evidence-based foundation for epistemic logic.
Abstract: We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t:F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. As a case study, we formalize Gettier examples in Justification Logic and reveal hidden assumptions and redundancies in Gettier reasoning. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidence-based foundation for epistemic logic.
TL;DR: It is shown that Jeffrey-Keynes algebras can be used to develop a theory of decision under uncertainty that measures the degree of belief on the quasi (or partial) truth of the propositions.
Abstract: In Tsuji 1997 the concept of Jeffrey-Keynes algebras was introduced in order to construct a paraconsistent theory of decision under uncertainty. In the present paper we show that these algebras can be used to develop a theory of decision under uncertainty that measures the degree of belief on the quasi (or partial) truth of the propositions. As applications of this new theory of decision, we use it to analyze Popper's paradox of ideal evidence and to indicate a possible way of formalizing Keynes' theory of economic action.
Proceedings Article•
01 Jan 1994
TL;DR: Relations between SLPs’ and BLP’ semantics are demonstrated, and it is argued that SLPs can encode the same knowledge as a subclass of BLPs, and extended SLPs are introduced which lift the latter result to any BLP.
Abstract: First-order probabilistic models are recognized as efficient frameworks to represent several realworld problems: they combine the expressive power of first-order logic, which serves as a knowledge representation language, and the capability to model uncertainty with probabilities. Among existing models, it is usual to distinguish the domain-frequency approach from the possible-worlds approach. Bayesian logic programs (BLPs, which conveniently encode possible-worlds semantics) and stochastic logic programs (SLPs, often referred to as a domain-frequency approach) are promising probabilistic logic models in their categories. This paper is aimed at comparing the respective expressive power of these frameworks. We demonstrate relations between SLPs’ and BLPs’ semantics, and argue that SLPs can encode the same knowledge as a subclass of BLPs. We introduce extended SLPs which lift the latter result to any BLP. Converse properties are reviewed, and we show how BLPs can define the same semantics as complete, range-restricted, non-recursive SLPs. Algorithms that translate BLPs into SLPs (and vice versa) are provided, as well as worked examples of the intertranslations of SLPs and BLPs.
01 Jan 2016
TL;DR: This chapter intends to clarify the whole project behind LFIs, explaining why and how contradiction and triviality cease to coincide, and why andHow contradiction ceases to coincide with inconsistency.
Abstract: This chapter intends to clarify the whole project behind LFIs, explaining why and how contradiction and triviality cease to coincide, and why and how contradiction ceases to coincide with inconsistency. It also intends to explain that there is no opposition to the classical stance, besides the awareness that ‘classical’ logic involves some hidden assumptions that are made clear in this chapter.
03 Dec 2022
TL;DR: In this article , a first-order version of BD2, called QBD2, with semantics based on an appropriate notion of partial structures is proposed. But the semantics are not defined in terms of the classical negation.
Abstract: Belnap-Dunn's relevance logic, BD, was designed seeking a suitable logical device for dealing with multiple information sources which sometimes may provide inconsistent and/or incomplete pieces of information. BD is a four-valued logic which is both paraconsistent and paracomplete. On the other hand, De and Omori while investigating what classical negation amounts to in a paracomplete and paraconsistent four-valued setting, proposed the expansion BD2 of the four valued Belnap-Dunn logic by a classical negation. In this paper, we reintroduce the logic BD2 by means of a primitive weak consistency operator $\copyright$. This approach allows us to state in a direct way that this is not only a Logic of Formal Inconsistency (LFI) but also a Logic of Formal Underterminedness (LFU). After presenting a natural Hilbert-style characterization of BD2 obtained by means of twist-structures semantics, we propose a first-order version of BD2 called QBD2, with semantics based on an appropriate notion of partial structures. We show that in QBD2, $\exists$ and $\forall$ are interdefinable in terms of the paracomplete and paraconsistent negation, and not by means of the the classical negation. Finally, a Hilbert-style calculus for QBD2 is presented, proving the corresponding and soundness and completeness theorems.