Abductive Reasoning in Intuitionistic Propositional Logic via Theorem Synthesis
Abstract
With help of a compact Prologbased 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 selfcontained literate Prolog program, the paper supports interactive exploration of its content and ensures full replicability of our results.
 Publication:

arXiv eprints
 Pub Date:
 May 2022
 arXiv:
 arXiv:2205.05728
 Bibcode:
 2022arXiv220505728T
 Keywords:

 Computer Science  Logic in Computer Science
 EPrint:
 Paper presented at the 38th International Conference on Logic Programming (ICLP 2022), 15 pages