Contextual Abductive Reasoning with Side-Effects

TL;DR

This paper introduces a formal framework for abductive reasoning that incorporates side-effects and background knowledge, motivated by psychological experiments on belief bias, and provides a declarative semantics with potential broad applications.

Contribution

It formalizes new abductive context definitions with declarative semantics, integrating side-effects and background knowledge, extending previous models and enabling richer reasoning capabilities.

Findings

Formalization of abductive contexts with side-effects

Introduction of declarative semantics for abductive reasoning

Application to psychological reasoning phenomena

Abstract

The belief bias effect is a phenomenon which occurs when we think that we judge an argument based on our reasoning, but are actually influenced by our beliefs and prior knowledge. Evans, Barston and Pollard carried out a psychological syllogistic reasoning task to prove this effect. Participants were asked whether they would accept or reject a given syllogism. We discuss one specific case which is commonly assumed to be believable but which is actually not logically valid. By introducing abnormalities, abduction and background knowledge, we adequately model this case under the weak completion semantics. Our formalization reveals new questions about possible extensions in abductive reasoning. For instance, observations and their explanations might include some relevant prior abductive contextual information concerning some side-effect or leading to a contestable or refutable side-effect. A weaker notion indicates the support of some relevant consequences by a prior abductive context. Yet another definition describes jointly supported relevant consequences, which captures the idea of two observations containing mutually supportive side-effects. Though motivated with and exemplified by the running psychology application, the various new general abductive context definitions are introduced here and given a declarative semantics for the first time, and have a much wider scope of application. Inspection points, a concept introduced by Pereira and Pinto, allows us to express these definitions syntactically and intertwine them into an operational semantics.