157 research outputs found
Kripke Models for Classical Logic
We introduce a notion of Kripke model for classical logic for which we
constructively prove soundness and cut-free completeness. We discuss the
novelty of the notion and its potential applications
Loop-free construction of counter-models for intuitionistic propositional logic
We present a non-looping method to construct Kripke trees refuting the non-theorems of intuitionistic propositional logic, using a contraction-free sequent calculus.União Europeia (UE) - project ESPRIT BRA 7232 GENTZEN.Junta Nacional de Investigação Científica e Tecnológica (JNICT)
Forward refutation for Gödel-Dummett Logics
We propose a refutation calculus to check the unprovability of a formula in Gödel-Dummett logics. From refutations we can directly extract countermodels for unprovable formulas, moreover the calculus is designed so to support a forward proof-search strategy that can be understood as a top-down construction of a model
Deductive Systems in Traditional and Modern Logic
The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic
Optimization techniques for propositional intuitionistic logic and their implementation
AbstractThis paper presents some techniques which bound the proof search space in propositional intuitionistic logic. These techniques are justified by Kripke semantics and are the backbone of a tableau based theorem prover (PITP) implemented in C++. PITP and some known theorem provers are compared using the formulas of ILTP benchmark library. It turns out that PITP is, at the moment, the propositional prover that solves most formulas of the library
Mathematical Logic: Proof theory, Constructive Mathematics
The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” was centered around proof-theoretic aspects of current mathematics, constructive mathematics and logical aspects of computational complexit
Achieving while maintaining:A logic of knowing how with intermediate constraints
In this paper, we propose a ternary knowing how operator to express that the
agent knows how to achieve given while maintaining
in-between. It generalizes the logic of goal-directed knowing how proposed by
Yanjing Wang 2015 'A logic of knowing how'. We give a sound and complete
axiomatization of this logic.Comment: appear in Proceedings of ICLA 201
Proof search and counter-model construction for bi-intuitionistic propositional logic with labelled sequents
Bi-intuitionistic logic is a conservative extension of
intuitionistic logic with a connective dual to implication, called
exclusion. We present a sound and complete cut-free labelled sequent
calculus for bi-intuitionistic propositional logic, BiInt,
following S. Negri's general method for devising sequent calculi
for normal modal logics. Although it arises as a natural
formalization of the Kripke semantics, it is does not directly
support proof search. To describe a proof search procedure, we
develop a more algorithmic version that also allows for
counter-model extraction from a failed proof attempt.Estonian Science Foundation - grants no. 5567; 6940Fundação para a Ciência e a Tecnologia (FCT)RESCUE - no. PTDC/EIA/65862/2006TYPES - FP6 ISTCentro de matemática da Universidade do Minh
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