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Abductive Reasoning in Intuitionistic Propositional Logic via Theorem Synthesis

Published online by Cambridge University Press:  28 June 2022

PAUL TARAU Open the ORCID record for PAUL TARAU [Opens in a new window]
PAUL TARAU*
Affiliation:
University of North Texas, Denton, TX 76203, USA (e-mail: [email protected])
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Abstract

With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic abductive reasoning mechanisms, we synthesize conjunctions of literals that mimic rows of truth tables in classical or intermediate logics and we abduce conditional hypotheses that turn the theorems of classical or intermediate logics into theorems in intuitionistic logic. One step further, we generalize our abductive reasoning mechanism to synthesize more expressive sequent premises using a minimal set of canonical formulas, to which arbitrary formulas in the calculus can be reduced while preserving their provability. Organized as a self-contained literate Prolog program, the paper supports interactive exploration of its content and ensures full replicability of our results.

Keywords

abductive reasoning in intuitionistic logictheorem synthesislogic programming and automated reasoningtheorem provers for intuitionistic propositional logicimplementing sequent calculi in Prolog
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 22 , Issue 5: 38th International Conference on Logic Programming Special Issue II , September 2022 , pp. 693 - 707
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

*

We thank the anonymous reviewers of ICLP’2022 for their constructive comments and suggestions.

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