A Gentzen Calculus for Nothing but the Truth

Wintein, Stefan; Muskens, Reinhard

doi:10.1007/s10992-015-9385-3

Cited by 12 publications

(7 citation statements)

References 12 publications

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“…First, logicians are concerned to establish that a given system has certain desirable properties. This can take the form of establishing a widely regarded beneficial property of logic, such as their decidability (Payne 2015; Wintein and Muskens 2016), but it also often takes the form of solving a non‐generic open problem for a particular logic (Badia 2018; Uckelman, Alama, and Knoks 2014). For instance, Slaney and Walker (2014) set about establishing that the pure implication fragment of Anderson and Belnap's (1975) logic T has infinitely many pairwise non‐equivalent formulae in one propositional variable; a particular instance of the problem set by Meyer (1970) for all substructural logics.…”

Section: Benefit 2: New Fruitful Areasmentioning

confidence: 99%

The philosophy of logical practice

Martin

2022

Metaphilosophy

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While we now have an increasingly detailed understanding of the varied goals and methods that constitute the sciences and mathematics, our understanding of logic as a research area lags behind. A significant reason for this deficiency is that, unlike in the philosophies of science and mathematics, philosophers of logic have yet to embrace a practice‐based approach to their field, re‐orientating their attention towards logic as it is actually practised by logicians. This paper makes the case for a new area of research, the philosophy of logical practice, to sit alongside traditional philosophy of logic and systematically investigate logic's aims and methodologies using the practice‐based approach.

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Section: Benefit 2: New Fruitful Areasmentioning

confidence: 99%

The philosophy of logical practice

Martin

2022

Metaphilosophy

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“…Third, we use our method to investigate the proof-theoretical consequences of including intuitive truth-functional implications in FDE-like logics. Lastly, we discuss related work by Baaz et al [6] and Wintein and Muskens [26] that shares some of our theoretical objectives but proposes different ways to realize them. A short summary and an open question conclude the paper.…”

Section: Introductionmentioning

confidence: 99%

Two-sided Sequent Calculi for FDE-like Four-valued Logics

Kooi

Tamminga

2022

J Philos Logic

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We present a method that generates two-sided sequent calculi for four-valued logics like first degree entailment (FDE). (We say that a logic is FDE-like if it has finitely many operators of finite arity, including negation, and if all of its operators are truth-functional over the four truth-values ‘none’, ‘false’, ‘true’, and ‘both’, where ‘true’ and ‘both’ are designated.) First, we show that for every n-ary operator ⋆ every truth table entry f⋆(x1,…,xn) = y can be characterized in terms of a pair of sequent rules. Secondly, we use these sequent rules to build sequent calculi and prove their completeness. With the help of two simplification procedures we then show that the 2 ⋅ 4n sequent rules that characterize an n-ary operator can be systematically reduced to at most four sequent rules. Thirdly, we use our method to investigate the proof-theoretical consequences of including intuitive truth-functional implications in FDE-like logics.

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“…In a recent paper, Pietz and Rivieccio [17] presented Exactly True Logic (ETL), an interesting variation upon FDE that is obtained by preserving exact truth, i.e. the value T, over all 4-valued valuations of L. Although both [17] and Wintein and Muskens [25] study ETL to quite some extent, no investigation of its interpolation property is to be found in the literature. We will first explain that the Maehara-style method cannot be invoked to construct interpolants for ETL.…”

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confidence: 99%

Interpolation Methods for Dunn Logics and Their Extensions

Wintein

Muskens

2017

Stud Logica

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Abstract.The semantic valuations of classical logic, strong Kleene logic, the logic of paradox and the logic of first-degree 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 Dunncalculus, a signed tableau calculus whose rules mirror the Dunn conditions syntactically and which characterizes the Dunn logics in a uniform way. In terms of the Dunn calculus, we first introduce two different interpolation methods, each of which uniformly shows that the Dunn logics have the interpolation property. One of the methods is closely related to Maehara's method but the other method, which we call the pruned tableau method, is novel to this paper. We provide various reasons to prefer the pruned tableau method to the Maehara-style method. We then turn our attention to extensions of Dunn logics with so-called appropriate implication connectives. Although these logics have been considered at various places in the literature, a study of the interpolation properties of these logics is lacking. We use the pruned tableau method to uniformly show that these extended Dunn logics have the interpolation property and explain that the same result cannot be obtained via the Maehara-style method. Finally, we show how the pruned tableau method constructs interpolants for functionally complete extensions of the Dunn logics.

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A Gentzen Calculus for Nothing but the Truth

Cited by 12 publications

References 12 publications

The philosophy of logical practice

The philosophy of logical practice

Two-sided Sequent Calculi for FDE-like Four-valued Logics

Interpolation Methods for Dunn Logics and Their Extensions

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