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Threevalued Logics in Modal Logic
"... Abstract. Every truthfunctional threevalued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any threevalued logic into a modal formula. S ..."
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Abstract. Every truthfunctional threevalued propositional logic can be conservatively translated into the modal logic S5. We prove this claim constructively in two steps. First, we define a Translation Manual that converts any propositional formula of any threevalued logic into a modal formula
CLASSIFICATION OF THREEVALUED LOGICAL FUNCTIONS PRESERVING 0
, 1990
"... The set To of threevalued logical functions preserving 0 is classified into 253 classes using the known classification of P3 (the whole set of threevalued logical functions). This enables one to determine all 883,720 classes of Tobases. ..."
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The set To of threevalued logical functions preserving 0 is classified into 253 classes using the known classification of P3 (the whole set of threevalued logical functions). This enables one to determine all 883,720 classes of Tobases.
Kleene’s threevalued logics and their children
 Fundamenta Informaticae
, 1994
"... Abstract. Kleene’s strong threevalued logic extends naturally to a fourvalued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it fourvalued analogs of Kleene’s weak threevalued logic, and the asymmetri ..."
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Abstract. Kleene’s strong threevalued logic extends naturally to a fourvalued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it fourvalued analogs of Kleene’s weak threevalued logic
Bourne on Future Contingents and Threevalued Logic∗
"... Recently, Bourne constructed a system of threevalued logic that he supposed to replace ÃLukasiewicz’s threevalued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to ÃLukasiewicz’s system. However, finding some good mo ..."
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Recently, Bourne constructed a system of threevalued logic that he supposed to replace ÃLukasiewicz’s threevalued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to ÃLukasiewicz’s system. However, finding some good
Gentzentype Refutation Systems for ThreeValued Logics ⋆
"... Abstract. While the purpose of a conventional proof calculus is to axiomatise the set of valid sentences of a given logic, a refutation system, or complementary calculus, is concerned with axiomatising the invalid sentences. Instead of exhaustively searching for counter models for some sentence, ref ..."
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, refutation systems establish invalidity by deduction and thus in a purely syntactic way. Such systems are relevant not only for prooftheoretic reasons but also for realising deductive systems for nonmonotonic logics. In this paper, we introduce Gentzentype refutation systems for two basic threevalued
Threevalued Logics for Inconsistency Handling
"... While threevalued paraconsistent logic is a valuable framework for reasoning under inconsistency, the corresponding basic inference relation is too cautious and fails in discriminating in a finegrained way the set of expected consequences of belief bases. To address both issues, we point out more ..."
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Cited by 9 (0 self)
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While threevalued paraconsistent logic is a valuable framework for reasoning under inconsistency, the corresponding basic inference relation is too cautious and fails in discriminating in a finegrained way the set of expected consequences of belief bases. To address both issues, we point out more
Maximally paraconsistent threevalued logics
 Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning (KR’10
, 2010
"... Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper, we introduce the strongest possible notion of maximal paraconsistency, and investigate it in th ..."
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Cited by 3 (1 self)
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it in the context of logics that are based on deterministic or nondeterministic threevalued matrices. We first show that most of the logics that are based on properly nondeterministic threevalued matrices are not maximally paraconsistent. Then we show that in contrast, in the deterministic case all the natural
Learning ThreeValued Logic Programs
, 1999
"... We show that the adoption of a threevalued setting for inductive concept learning is particularly useful for learning. Distinguishing between what is true, what is false and what is unknown can be useful in situations where decisions have to be taken on the basis of scarce information. In order to ..."
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to learn in a threevalued setting, we adopt Extended Logic Programs (ELP) under a WellFounded Semantics with explicit negation (WFSX ) as the representation formalism for learning. Standard Inductive Logic Programming techniques are then employed to learn the concept and its opposite. The learnt
Probabilistic Inference on ThreeValued Logic
 Proceedings of 9th International Conferece on Rough Sets, Fuzzy Sets, Data Mining, and GranularSoft Computing (RSFDGrc’2003
, 2003
"... In this paper, we extend Nilsson's probabilistic logic [1] to allow that each sentence S has three sets of possible worlds. We adopt the ideas of consistency and possible worlds introduced by Nilsson in [1], but propose a new method called linear equation method to deal with the problems of ..."
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In this paper, we extend Nilsson's probabilistic logic [1] to allow that each sentence S has three sets of possible worlds. We adopt the ideas of consistency and possible worlds introduced by Nilsson in [1], but propose a new method called linear equation method to deal with the problems
Kleene’s threevalued logic and process algebra
, 1997
"... We propose a combination of Kleene’s threevalued logic and ACP process algebra via the guarded command construct. We present an operational semantics in SOSstyle, and a completeness result. Ó 1998 Elsevier Science B.V. All rights reserved. ..."
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We propose a combination of Kleene’s threevalued logic and ACP process algebra via the guarded command construct. We present an operational semantics in SOSstyle, and a completeness result. Ó 1998 Elsevier Science B.V. All rights reserved.
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