Citations of:
Systematic construction of natural deduction systems for manyvalued logics
In Proceedings of The TwentyThird International Symposium on MultipleValued Logic, 1993. Los Alamitos, CA: IEEE Press. pp. 208213 (1993)
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This paper develops and motivates a paraconsistent approach to semantic paradox from within a modest inferentialist framework. I begin from the bilateralist theory developed by Greg Restall, which uses constraints on assertions and denials to motivate a multipleconclusion sequent calculus for classical logic, and, via which, classical semantics can be determined. I then use the addition of a transparent truthpredicate to motivate an intermediate speechact. On this approach, a liarlike sentence should be “weakly asserted”, involving a commitment to the sentence (...) 

The starting point of this paper is a version of intratheoretical pluralism that was recently proposed by Hjortland [2013]. In a first move, I use synonymyrelations to formulate an intuitively compelling objection against Hjortland's claim that, if one uses a single calculus to characterise the consequence relations of the paraconsistent logic LP and the paracomplete logic K3, one immediately obtains multiple consequence relations for a single language and hence a reply to the Quinean charge of meaning variance. In a second (...) 

In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti and Reichenbach on the one hand, and by Cooper and Cantwell on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT allows for (...) 

Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaningvariance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaningvariance, both in general and (...) 

We study structural rules in the context of multivalued logics with finitelymany truthvalues. We first extend Gentzen’s traditional structural rules to a multivalued logic context; in addition, we propos some novel structural rules, fitting only multivalued logics. Then, we propose a novel definition, namely, structural rules completeness of a collection of structural rules, requiring derivability of the restriction of consequence to atomic formulas by structural rules only. The restriction to atomic formulas relieves the need to concern logical rules in the (...) 

The proof theory of manyvalued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of manyvalued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finitevalued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finitevalued first order (...) 

In [5], Béziau provides a means by which Gentzen’s sequent calculus can be combined with the general semantic theory of bivaluations. In doing so, according to Béziau, it is possible to construe the abstract “core” of logics in general, where logical syntax and semantics are “two sides of the same coin”. The central suggestion there is that, by way of a modification of the notion of maximal consistency, it is possible to prove the soundness and completeness for any normal logic. (...) 

In this paper we consider possibilities for applying padic valued logic BL to the task of designing an unconventional computer based on the medium of slime mould, the giant amoebozoa that looks for attractants and reaches them by means of propagating complex networks. If it is assumed that at any time step t of propagation the slime mould can discover and reach not more than attractants, then this behaviour can be coded in terms of padic numbers. As a result, this (...) 

Methods available for the axiomatization of arbitrary finitevalued logics can be applied to obtain sound and complete intelim rules for all truthfunctional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) 