Abstract. Every truth-functional three-valued 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 three-valued logic into a modal formula

The set To of three-valued logical functions preserving 0 is classified into 253 classes using the known classification of P3 (the whole set of three-valued logical functions). This enables one to determine all 883,720 classes of To-bases.

Abstract. Kleene’s strong three-valued logic extends naturally to a four-valued 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 four-valued analogs of Kleene’s weak three-valued logic

Recently, Bourne constructed a system of three-valued logic that he supposed to replace ÃLukasiewicz’s three-valued logic in view of the prob-lems 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

, refutation systems establish invalidity by deduction and thus in a purely syntactic way. Such systems are relevant not only for proof-theoretic reasons but also for realising deductive systems for nonmonotonic logics. In this paper, we introduce Gentzen-type refutation systems for two basic three-valued

While three-valued paraconsistent logic is a valuable framework for reasoning under inconsistency, the corresponding basic inference relation is too cautious and fails in discriminating in a fine-grained way the set of expected consequences of belief bases. To address both issues, we point out more

it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We first show that most of the logics that are based on properly non-deterministic three-valued matri-ces are not maximally paraconsistent. Then we show that in contrast, in the deterministic case all the natural

to learn in a three-valued setting, we adopt Extended Logic Programs (ELP) under a Well-Founded 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

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

We propose a combination of Kleene’s three-valued logic and ACP process algebra via the guarded command construct. We present an operational semantics in SOS-style, and a completeness result. Ó 1998 Elsevier Science B.V. All rights reserved.