On the relation between possibilistic logic and modal logics of belief and knowledge

  title={On the relation between possibilistic logic and modal logics of belief and knowledge},
  author={Mohua Banerjee and Didier Dubois and Llu{\'i}s Godo and Henri Prade},
  journal={Journal of Applied Non-Classical Logics},
  pages={206 - 224}
Abstract Possibilistic logic and modal logic are knowledge representation frameworks sharing some common features, such as the duality between possibility and necessity, and the decomposability of necessity for conjunctions, as well as some obvious differences since possibility theory is graded. At the semantic level, possibilistic logic relies on possibility distributions and modal logic on accessibility relations. In the last 30 years, there have been a series of attempts for bridging the two… 
Possibilistic Logic: From Certainty-Qualified Statements to Two-Tiered Logics - A Prospective Survey
A survey of its main developments and applications in artificial intelligence, together with a short presentation of works in progress is proposed, which relies on a sound alliance between classical logic and possibility theory which offers an accurate modeling of partial ignorance.
A Crash Course on Generalized Possibilistic Logic
It is shown that three traditions of reasoning under or about uncertainty can be reconciled in the setting of possibility theory, and basic possibilistic logic is offered, and of its generalisation that comes close to a modal logic albeit with simpler more natural epistemic semantics.


Modal logics for qualitative possibility theory
Stable Models in Generalized Possibilistic Logic
An axiomatization is introduced showing that GPL is a fragment of a graded version of the modal logic KD, and soundness and completeness are proved, and a close link is revealed between the well-known stable model semantics for logic programming and the notion of minimally specific models in GPL.
Generalized possibilistic logic: Foundations and applications to qualitative reasoning about uncertainty
Possibilistic vs. Relational Semantics for Logics of Incomplete Information
An extension of the MEL logic to a language containing modal formulae of depth 0 or 1 only is proposed, and has the same axioms as, and is in some sense equivalent to, S5 with a restricted language, but with the same expressive power.
A simple logic for reasoning about incomplete knowledge
Possibilistic logic: a retrospective and prospective view
A Simple Modal Logic for Reasoning about Revealed Beliefs
It is proved that any family of non-empty subsets of interpretations can be expressed as a single formula in MEL, and this formula is a symbolic counterpart of the Mobius transform in the theory of belief functions.
A Logic of Graded Possibility and Certainty Coping with Partial Inconsistency
An internal semantics for modal logic
This work uses the idea of possible worlds, but by directly describing the “internal semantics” of each possible world, to introduce modal structures as models for modal logic.
Reasoning about Uncertainty and Explicit Ignorance in Generalized Possibilistic Logic
This paper studies two types of approaches for reasoning about ignorance in GPL based on the idea of minimal specificity and on the notion of guaranteed possibility, respectively, and shows how these approaches naturally lead to different flavours of the language of GPL and a number of decision problems.