A Formal Framework for Synthesis and Verification of Logic Programs

ACM Trans. Comput. Logic

Fiorino

2005

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In this article we study the complexity of disjunction property for intuitionistic logic, the modal logics S4, S4.1, Grzegorczyk logic, Gödel-Löb logic, and the intuitionistic counterpart of the modal logic K. For S4 we even prove the feasible interpolation theorem and we provide a lower bound for the length of proofs. The techniques we use do not require proving structural properties of the calculi in hand, such as the cut-elimination theorem or the normalization theorem. This is a key point of our approach, since it allows us to treat logics for which only Hilbert-style characterizations are known.

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“…Extraction calculi have also been applied in the framework of program synthesis from formal proofs; see Avellone et al [2001]; Ferrari et al [1999].…”

Section: The Notation πmentioning

confidence: 99%

On the complexity of the disjunction property in intuitionistic and modal logics

ACM Trans. Comput. Logic

Fiorino

2005

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“…Such a class contains formal systems that cannot be treated with Normalization, Cutelimination or Realizability. Extraction calculi have also been applied in the framework of program synthesis from formal proofs, see [1,6].…”

Section: Definition 1 (Extraction Calculus)mentioning

confidence: 99%

On the Complexity of Disjunction and Explicit Definability Properties in Some Intermediate Logics

Logic for Programming, Artificial Intelligence, and Reasoning

Fiorino

2002

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Abstract. In this paper we provide a uniform framework, based on extraction calculi, where to study the complexity of the problem to decide the disjunction and the explicit definability properties for Intuitionistic Logic and some Superintuitionistic Logics. Unlike the previous approaches, our framework is independent of structural properties of the proof systems and it can be applied to Natural Deduction systems, Hilbert style systems and Gentzen sequent systems.

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Untitled

2003

Studia Logica