Citations of:
On Partial and Paraconsistent Logics
Notre Dame Journal of Formal Logic 40 (3):352374 (1999)
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On the sidelines of classical logic, many partial and paraconsistent threevalued logics have been developed. Most of them differ in the notion of logical consequence or in the definition of logical connectives. This article aims, firstly, to provide both a modeltheoretic and a prooftheoretic unified framework for these logics and, secondly, to apply these general frameworks to several wellknown threevalued logics. The prooftheoretic approach to which we give preference is sequent calculus. In this perspective, several results concerning the properties of (...) 

In their paper Nothing but the Truth Andreas Pietz and Umberto Rivieccio present Exactly True Logic, an interesting variation upon the fourvalued logic for firstdegree entailment FDE that was given by Belnap and Dunn in the 1970s. Pietz & Rivieccio provide this logic with a Hilbertstyle axiomatisation and write that finding a nice sequent calculus for the logic will presumably not be easy. But a sequent calculus can be given and in this paper we will show that a calculus for (...) 

We define the paraconsistent supralogic Pσ by a typeshift from the booleans o of propositional logic Po to the suprabooleans σ of the propositional type logic P obtained as the propositional fragment of the transfinite type theory Q defined by Peter Andrews as a classical foundation of mathematics. The supralogic is in a sense a propositional logic only, but since there is an infinite number of suprabooleans and arithmetical operations are available for this and other types, virtually anything can be (...) 

One of the problems we face in manyvalued logic is the difficulty of capturing the intuitive meaning of the connectives introduced through truth tables. At the same time, however, some logics have nice ways to capture the intended meaning of connectives easily, such as fourvalued logic studied by Belnap and Dunn. Inspired by Dunn’s discovery, we first describe a mechanical procedure, in expansions of BelnapDunn logic, to obtain truth conditions in terms of the behavior of the Truth and the False, (...) 

According to Suszko's Thesis, there are but two logical values, true and false. In this paper, R. Suszko's, G. Malinowski's, and M. Tsuji's analyses of logical twovaluedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation. 

The semantic valuations of classical logic, strong Kleene logic, the logic of paradox and the logic of firstdegree entailment, all respect the Dunn conditions: we call them Dunn logics. In this paper, we study the interpolation properties of the Dunn logics and extensions of these logics to more expressive languages. We do so by relying on the \ calculus, a signed tableau calculus whose rules mirror the Dunn conditions syntactically and which characterizes the Dunn logics in a uniform way. In (...) 

By using the notions of exact truth and exact falsity, one can give 16 distinct definitions of classical consequence. This paper studies the class of relations that results from these definitions in settings that are paracomplete, paraconsistent or both and that are governed by the Strong Kleene schema. Besides familiar logics such as Strong Kleene logic, the Logic of Paradox and First Degree Entailment, the resulting class of all Strong Kleene generalizations of classical logic also contains a host of unfamiliar (...) 