Abductive Reasoning in Intuitionistic Propositional Logic via Theorem Synthesis

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.

Kemampuan Penalaran Abduktif Siswa Ditinjau dari Gaya Belajar

“…Walton (2014) menyatakan bahwa solusi pemecahan masalah yang diperoleh dalam penalaran abduktif dianggap yang terbaik daripada penalaran deduktif atau induktif, karena didasarkan pada pemikiran yang paling masuk akal. Dipertegas Tarau (2022) yang menyatakan bahwa kemampuan penalaran abduktif dapat digunakan pada berbagai jenis permasalahan, karena premis-premis yang dihasilkan berdasarkan asumsi yang logis.…”