Propositional Logic, Modal Logic and Temporal Logic Definition The syntax of propositional logics is defined as φ ::= p | ¬φ | φ ∨ φ | φ ∧ φ where p ranges over a (finite) set of atomic propositions AP. The semantics is given by truth tables, e.g., for p ∧ q: ∧ > ⊥ > > ⊥ ⊥ ⊥ ⊥ Propositional Logic, Modal Logic and Temporal Logic Definition The syntax of propositional logics is defined as φ ::= p...

Abduction is a form of nonmonotonic reasoning that looks for an explanation for an observed manifestation according to some knowledge base. One form of the abduction problem studied in the literature is the propositional abduction problem parameterized by a structure Γ over the two-element domain. In that case, the knowledge base is a set of constraints over Γ, the manifestation and explanation...

Reasoning with propositional knowledge based on fuzzy neural logic" (1996). In this article, a new kind of reasoning for propositional knowledge, which is based on the fuzzy neural logic initialed by Teh, is introduced. A fundamental theorem is presented showing that any fuzzy neural logic network can be represented by operations: bounded sum, complement, and scalar product. Propositional calcu...

We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover a variety of plate models and of probabilistic relational models. We study the complexity of inferences when network, query and domain are the input (the inf...

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorith...

Levesque introduced the notion of only-knowing to precisely capture the beliefs of a knowledge base. He also showed how only-knowing can be used to formalize non-monotonic behavior within a monotonic logic. Despite its appeal, all attempts to extend only-knowing to the many agent case have undesirable properties. A belief model by Halpern and Lakemeyer, for instance, appeals to proof-theoretic ...

We study the computational properties of the propositional fragment of MBNF , the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries and logic programming. We characterize the complexity and provide algorithms...