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Proving infinitary formulas

Published online by Cambridge University Press:  14 October 2016

AMELIA HARRISON ,
VLADIMIR LIFSCHITZ  and
JULIAN MICHAEL
AMELIA HARRISON
Affiliation:
University of Texas, Austin, Texas, USA (e-mail: ameliaj@cs.utexas.edu, vl@cs.utexas.edu)
VLADIMIR LIFSCHITZ
Affiliation:
University of Texas, Austin, Texas, USA (e-mail: ameliaj@cs.utexas.edu, vl@cs.utexas.edu)
JULIAN MICHAEL
Affiliation:
University of Washington, Seattle, Washington, USA (e-mail: julianjohnmichael@gmail.com)
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Abstract

The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic exists, but a proof in that system may include infinitely many formulas. In this note we describe a relationship between the validity of infinitary formulas in the logic of here-and-there and the provability of formulas in some finite deductive systems. This relationship allows us to use finite proofs to justify the validity of infinitary formulas.

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 16 , Special Issue 5-6: 32nd International Conference on Logic Programming , September 2016 , pp. 787 - 799
Copyright
Copyright © Cambridge University Press 2016 

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