A Primer for Preferential Non-Monotonic Propositional Team Logics

TL;DR

This work introduces preferential (KLM-style) non-monotonic reasoning within propositional team logics, defining standard preferential models and analyzing how they govern non-monotonic entailment. It shows that System $C$ holds for preferential team logics, but the $Or$-rule—and thus System $P$—may fail unless additional conditions (star-property, triangle-property) are satisfied. A key contribution is the precise characterization of when preferential dependence logics satisfy System $P$, proving equivalences among semantic properties and showing that, under these conditions, preferential entailment reduces to classical (singleton) or flattened entailment. The paper also relates preferential entailment to classical and to dependence-logic entailment via flattening, and presents canonical sub- and super-models that realize different entailment notions. These results provide a foundational primer for further study of non-monotonic reasoning in team semantics, including extensions to other axiom systems and complexity considerations.

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.

Theorems & Definitions (31)

• Definition 1: Classical propositional logic ($\mathsf{PL}$)
• Definition 2
• Definition 3: Team semantics of $\mathsf{PL}$
• Proposition 4
• Proposition 5
• Example 6
• Definition 7
• Definition 8
• Proposition 9: ? ?
• Definition 10