Modal logics with Belnapian truth values
TLDR
Various four- and three-valued modal propositional logics are studied and axiom systems are defined and shown to be sound and complete with respect to the relational semantics and to twist structures over modal algebras.Abstract:
Various four- and three-valued modal propositional logics are studied. The basic systems are modal extensions BK and BS4 of Belnap and Dunn's four-valued logic of firstdegree entailment. Three-valued extensions of BK and BS4 are considered as well. These logics are introduced semantically by means of relational models with two distinct evaluation relations, one for verification (support of truth) and the other for falsification (support of falsity). Axiom systems are defined and shown to be sound and complete with respect to the relational semantics and with respect to twist structures over modal algebras. Sound and complete tableau calculi are presented as well. Moreover, a number of constructive non-modal logics with strong negation are faithfully embedded into BS4, into its three-valued extension B3S4, or into temporal BS4, BtS4. These logics include David Nelson's three-valued logic N3, the four-valued logic N4 bottom, the connexive logic C, and several extensions of bi-intuitionistic logic by strong ...read more
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Федеральное государственное бюджетное учреждение «Научно-исследовательский институт комплексных проблем сердечно-сосудистых заболеваний» Сибирского отделения Российской академии медицинских наук, Кемерово, Россия
E. N. Usoltseva,Federal State +1 more
TL;DR: In this article, the authors proposed a method to improve the quality of the information provided by the user by using the information from the user's profile and the user profile of the service provider.
Journal ArticleDOI
40 years of FDE: An Introductory Overview
Hitoshi Omori,Heinrich Wansing +1 more
TL;DR: This introduction to the special issue “40 years of FDE” offers an overview of the field and put the papers included in the specialissue into perspective and presents various semantics and proof systems for FDE.
Journal Article
Four-valued modal logic: Kripke semantics and duality.
Achim Jung,Umberto Rivieccio +1 more
TL;DR: The aim is to study the least modal logic over the Belnap lattice, that is, the logic determined by the class of all Kripke frames where the accessibility relation as well as semantic valuations are four-valued.
Journal ArticleDOI
Disentangling FDE-Based Paraconsistent Modal Logics
TL;DR: The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated and MBL can be faithfully embedded into the bimodal logic over the non-modal vocabulary of MBL.
Journal ArticleDOI
Four-valued modal logic: Kripke semantics and duality
TL;DR: In this paper, the authors define and axiomatize the least modal logic over the four-element Belnap lattice, which is the logic determined by the class of all Kripke frames where the accessibility relation as well as semantic valuations are four-valued.
References
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Book ChapterDOI
A Useful Four-Valued Logic
TL;DR: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead to irrelevant conclusions.
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TL;DR: In this paper, the authors propose a tableau-based approach to show that an argument A may entail B because of some feature of A alone, irrespective of B, and vice versa.
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