General Proof Theory: Introduction

Piecha, Thomas; Schroeder‐Heister, Peter

doi:10.1007/s11225-018-9818-4

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The Classic Proof-theoretic Approach1

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2024

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Cited by 3 publications

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“…The "classic approach" to the design of a Hoare style logic follows the proof-theoretic semantics in logic originated by Hilbert, Gentzen, Prawitz, and others [70]. The true program properties are the provable ones, which is also the idea of "axiomatic semantics" [95], that is, Floyd's idea that a program proof method is "Assigning Meaning to Programs" [42].…”

Section: The Classic Proof-theoretic Approachmentioning

confidence: 99%

Calculational design of a regular model checker by abstract interpretation

Cousot¹

2021

Theoretical Computer Science

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Section: The Classic Proof-theoretic Approachmentioning

confidence: 99%

Calculational design of a regular model checker by abstract interpretation

Cousot¹

2021

Theoretical Computer Science

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A logic for best explanations

Millson

Straßer

2019

Journal of Applied Non-Classical Logics

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Calculational Design of [In]Correctness Transformational Program Logics by Abstract Interpretation

Cousot

2024

Proc. ACM Program. Lang.

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We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a natural relational semantics covering both finite and infinite executions. This understanding of logics as abstractions of a semantics facilitates their comparisons through their respective abstractions of the semantics (rather that the much more difficult comparison through their formal proof systems). More importantly, the formalization provides a calculational method for constructively designing the sound and complete formal proof system by abstraction of the semantics. As an example, we extend Hoare logic to cover all possible behaviors of nondeterministic programs and design a new precondition (in)correctness logic.

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General Proof Theory: Introduction

Abstract: This special issue on general proof theory collects papers resulting from the conference on general proof theory held in November 2015 in Tübingen.

Cited by 3 publications

References 18 publications

Calculational design of a regular model checker by abstract interpretation

Calculational design of a regular model checker by abstract interpretation

A logic for best explanations

Calculational Design of [In]Correctness Transformational Program Logics by Abstract Interpretation

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