Proof Systems for Reasoning about Computation Errors

In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parall...

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Bibliographic Details
Published in:Studia logica Vol. 91; no. 2; pp. 273 - 293
Main Authors: Avron, Arnon, Konikowska, Beata
Format: Journal Article
Language:English
Published: Dordrecht Springer 01.03.2009
Springer Netherlands
Subjects:
Computational Linguistics
Determinism
Education
Error rates
Logic
Logical disjunction
Logical theorems
Mathematical Logic and Foundations
Philosophy
Reasoning
Semantics
Sequent calculus
Sequents
Truth tables
parallel computation
four-valued logics
non-deterministic matrices
computation errors
lazy sequential computation
sequent calculi
three-valued logics
ISSN:0039-3215, 1572-8730
Online Access:Get full text
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Summary:In the paper we examine the use of non-classical truth values for dealing with computation errors in program specification and validation. In that context, 3-valued McCarthy logic is suitable for handling lazy sequential computation, while 3-valued Kleene logic can be used for reasoning about parallel computation. If we want to be able to deal with both strategies without distinguishing between them, we combine Kleene and McCarthy logics into a logic based on a non-deterministic, 3-valued matrix, incorporating both options as a non-deterministic choice. If the two strategies are to be distinguished, Kleene and McCarthy logics are combined into a logic based on a 4-valued deterministic matrix featuring two kinds of computation errors which correspond to the two computation strategies described above. For the resulting logics, we provide sound and complete calculi of ordinary, two-valued sequents.
ISSN:0039-3215
1572-8730
DOI:10.1007/s11225-009-9175-4