A Primer for Preferential Non-Monotonic Propositional Team Logics

TL;DR

This paper explores preferential non-monotonic reasoning within propositional team semantics, establishing how team-based propositional logics lead to cumulative non-monotonic entailment and characterizing models satisfying System P postulates.

Contribution

It provides a formal characterization of preferential models in propositional dependence logic and connects classical and dependence logic entailments through preferential models.

Findings

Team-based propositional logics induce cumulative non-monotonic entailment.

Characterization of preferential models satisfying System P postulates.

Expressibility of classical and dependence logic entailments via preferential models.

Abstract

This paper considers KLM-style preferential non-monotonic reasoning in the setting of propositional team semantics. We show that team-based propositional logics naturally give rise to cumulative non-monotonic entailment relations. Motivated by the non-classical interpretation of disjunction in team semantics, we give a precise characterization for preferential models for propositional dependence logic satisfying all of System P postulates. Furthermore, we show how classical entailment and dependence logic entailment can be expressed in terms of non-trivial preferential models.