Bipolar logic and probabilistic interpretation

Abstract

Purpose

The paper aims to answer the question “can the bipolar Negative‐Neutral‐Positive logic be extended and motivated in some probabilistic framework?”

Design/methodology/approach

Using the context of cognitive map interpretation of the conjunction and disjunction connectives in bipolar logic, three probabilistic causal reasoning have been put forward. The first one is based on the infinitesimal representation of material implication while the second one relies on the qualitative representation developed by Suppes and Cartwright. In both cases special conditions for transitivity of inference and multiple inputs scenarios are examined. The third developed approach implicitly omits the cognitive interpretation and rather relies on the idea that the causal independence structure can be substituted by some functional that combines independent inputs in such a way to force the output to be in full agreement with results expected through the conjunctive and disjunctive connectives.

Findings

The paper reports several theoretical findings regarding the different conditions ensuring the agreement and equivalence between the bipolar logic connectives and their probabilistic counterparts for each proposal. The paper also provides useful insights to link the finding to probabilistic argumentation system where pro and con arguments are considered simultaneously.

Originality/value

The paper offers theoretical basis for researchers investigating different categories of logics and contribute to the discussion linking logic to probability.

Citation

Oussalah, M. (2005), "Bipolar logic and probabilistic interpretation", Kybernetes, Vol. 34 No. 9/10, pp. 1349-1383. https://doi.org/10.1108/03684920510614713