Abstract We study the lattice of extensions four-valued Belnap–Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. describe global structure this splitting it into several subintervals, and prove some new completeness theorems for The crucial technical tool purpose will be so-called antiaxiomatic (or explosive) part operator. logic turn out to particular interest ...

This paper shows some interesting properties of Kleene’s threevalued logic in relation to abductive reasoning. A semantical characterization of abductive explanations is proposed, based on the notion of minimal three-valued model. This establishes a relation between the minimization problem in abductive reasoning and three-valued semantics, in the same sense as non-monotonic reasoning deals wit...

this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...

Software model-checking based on the CEGAR framework can be made more precise by separating non-determinism from the lack of information due to abstraction. The two can be modeled individually using four-valued Belnap logic. In addition, this logic allows reasoning about negations effectively and thus enables checking of full CTL. In this paper, we present YASM – a new symbolic software model-c...

A method to perform diagnostic test generation in sequential circuits by modifying a conventional test generator is presented. The method utilizes circuit netlist modification along with a forced value at a primary input in the modified circuit. Techniques to reduce the computational effort for diagnostic test pattern generation in sequential circuits are also presented. Speed-up of the diagnos...

We investigate axiomatizations of Kripke’s [18] theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman’s axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke’s semantics in the straightforward sense; only the sentences provably true in KF are valid in Kripke’s partial ...