Some logics of belief and disbelief

@inproceedings{Chopra2002SomeLO,
  title={Some logics of belief and disbelief},
  author={Samir Chopra and Johannes Heidema and T. Meyer},
  booktitle={NMR},
  year={2002}
}
The introduction of explicit notions of rejection, or disbelief, in logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the explicit recording of classic belief contraction operations in the area of belief change, and the additional levels of expressivity obtained from an extended version of belief change which includes disbelief contraction. In this paper we present four logics of… 
Comparing Strengths of Beliefs Explicitly
TLDR
Formulas p > B q and p ≥ B q are introduced in the existing logical framework for discussing beliefs to express that the strength of belief in p is greater than (or equal to) that in q to aid in defining several other concepts in a uniform way.
A Qualitative Approach to Uncertainty
TLDR
A dual modal framework is introduced that discusses the different possibilities of an agent's attitude towards a proposition that can be expressed in this framework, and provides a preliminary look at the dynamics of the situation.
ENTAILMENT, DUALITY, AND THE FORMS OF REASONING
We explore the notion of duality for defeasible entailment relations induced by preference orderings on states. We then show that such preferential entailment relations may be used to characterise
Contracting Intuitionistic Theories
TLDR
The extent to which the two main methods of partial meet contraction and safe contraction can be employed for theories closed under intuitionistic consequence is investigated.
Beyond the Rational Explanation
In this paper, we generalise recent work on reconstructing an agent's epistemic state from observations about what it believed after receiving a series of revision inputs. We do so by also allowing

References

SHOWING 1-10 OF 25 REFERENCES
Changes of disjunctively closed bases
An operator of contraction for a belief set (a theory) can be obtained by assigning to it a belief base and an operator of partial meet contraction for that base. It is argued that closure of the
On the Logic of Acceptance and Rejection
The logic of acceptance and rejection (AEL2) is a nonmonotonic formalism to represent states of knowledge of an introspective agent making decisions about available information. Though having much in
Non-Prioritized Ranked Belief Change
TLDR
This paper replaces the linear ordering with a preference ranking on inputs from which a total preorder on inputs can be induced, and provides a semantic solution to the problem of dealing with inputs of equal rank.
A Logic for Default Reasoning
  • R. Reiter
  • Philosophy, Computer Science
    Artif. Intell.
  • 1980
On the logic of theory change: Partial meet contraction and revision functions
TLDR
The authors investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated, and basic properties of these functions are established.
A New Introduction to Modal Logic
TLDR
This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic with all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing clarity of exposition and approachability.
Fibring Non-Truth-Functional Logics: Completeness Preservation
TLDR
It is shown that this extended notion of fibring preserves completeness under certain reasonableconditions and is obtained using new techniques that explore the properties of a suitable meta-logic (conditional equational logic) where the (possibly) non-truth-functional valuations are specified.
Belief States as Default Theories: Studies in Non-Prioritized Belief Change
Change, choice and inference
Knowledge in flux: modeling the dynamics of epistemic states
...
...