Proof by analogy in mural

Analogy, explanation, and proof

People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic) whose truth was not even known prior to the existence of the explanation (proof). What do the cognitive operations underlying the inference that t...

Modi cation in Analogy-Driven Proof-Plan Construction

Analogy in Farabi's Thought

Thinkers and philosophers have constantly benefited from different         approaches of reasoning to explore and justify their ideas. Theses reasoning            approaches are considered as the principle instruments in speculative activities of the thinkers. To this end to achieve the procedure of thinking and the way philosophers achieve objectives, it is necessary to recognize their reasoni...

A Model of Analogy-Driven Proof-Plan Construction

This paper addresses a model of analogy-driven theorem proving that is more general and cognitively more adequate than previous approaches. The model works at the level of proof-plans. More precisely, we consider analogy as a control strategy in proof planning that employs a source proof-plan to guide the construction of a proof-plan for the target problem. Our approach includes a reformulation...

Reasoning by Analogy via Abstraction Reasoning by Analogy via Abstraction

theoremsnametheoremlenabs ag+ ag ag& ag"lemmasass ]x ] (y ] z) = (x ] y) ] z150.71 0.65 0.65 0.78com ]x ] y = y ] x230.92 0.79 0.3{lemc ]com2 ] x ] (y ] z) = y ] (x ] z)150.71 0.65{{lemc ]lemc ] ? ] (y ] x) = y ] ( ? ] x)130.76 0.48 0.40{even ]e(x) e(x ] y)290.82 1.00{{dbl...