Reducing Nondeterminism in the Calculus of Structures

Kahramanoğulları, Ozan

doi:10.1007/11916277_19

Cited by 13 publications

(7 citation statements)

References 14 publications

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“…We believe that the technique here generalizes to these other systems. For instance, in [28,27], we have shown that in BV the switch rule can be replaced with the rule lis without losing completeness. However, in BV and its extensions, the non-trivial interactions between commutative and non-commutative contexts make it difficult to extend these ideas to non-commutative context management rule of this logic.…”

Section: Discussionmentioning

confidence: 99%

Interaction and Depth against Nondeterminism in Proof Search

Kahramanoğulları¹

2014

Logical Methods in Computer Science

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Abstract. Deep inference is a proof theoretic methodology that generalizes the standard notion of inference of the sequent calculus, whereby inference rules become applicable at any depth inside logical expressions. Deep inference provides more freedom in the design of deductive systems for different logics and a rich combinatoric analysis of proofs. In particular, construction of exponentially shorter analytic proofs becomes possible, however with the cost of a greater nondeterminism than in the sequent calculus. In this paper, we show that the nondeterminism in proof search can be reduced without losing the shorter proofs and without sacrificing proof theoretic cleanliness. For this, we exploit an interaction and depth scheme in the logical expressions. We demonstrate our method on deep inference systems for multiplicative linear logic and classical logic, discuss its proof complexity and its relation to focusing, and present implementations.

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Section: Discussionmentioning

confidence: 99%

Interaction and Depth against Nondeterminism in Proof Search

Kahramanoğulları¹

2014

Logical Methods in Computer Science

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“…System implementations for this formalism have been already developed (Kahramanogulları [13,14,15]) and concern systems for propositional logic and variants of linear logic. We expect that some of the techniques applied in those systems will also apply in the modal systems.…”

Section: Discussionmentioning

confidence: 99%

A Deep Inference System for the Modal Logic S5

Stouppa

2007

Stud Logica

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We present a cut-admissible system for the modal logic S5 in a formalism that makes explicit and intensive use of deep inference. Deep inference is induced by the methods applied so far in conceptually pure systems for this logic. The system enjoys systematicity and modularity, two important properties that should be satisfied by modal systems. Furthermore, it enjoys a simple and direct design: the rules are few and the modal rules are in exact correspondence to the modal axioms.

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“…As shown in [Bruscoli and Guglielmi 2009], Frege systems and calculus of structures (with cut) p-simulate each other and are therefore equally powerful with respect to proof complexity. However, unlike Frege systems, the calculus of structures is a proof formalism that comes with methods for proof search [Kahramanogulları 2006;Chaudhuri et al 2011;Chaudhuri 2013b] and proof normalization [Brünnler 2003a;Brünnler 2006;. This means that we can now study cut-free proof systems with extension and substitution [Straßburger 2012].…”

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confidence: 99%

On the Power of Substitution in the Calculus of Structures

Novaković¹,

Straßburger

2015

ACM Trans. Comput. Logic

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There are two contributions in this paper. First, we give a direct proof of the known fact that Frege systems with substitution can be p-simulated by the calculus of structures extended with the substitution rule. This is done without referring to the p-equivalence of extended Frege systems and Frege systems with substitution. Second, we then show that the cut-free calculus of structures with substitution is p-equivalent to the cut-free calculus of structures with extension.

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Reducing Nondeterminism in the Calculus of Structures

Cited by 13 publications

References 14 publications

Interaction and Depth against Nondeterminism in Proof Search

Interaction and Depth against Nondeterminism in Proof Search

A Deep Inference System for the Modal Logic S5

On the Power of Substitution in the Calculus of Structures

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