Computing certain answers is the preferred way of answering queries in scenarios involving incomplete data. This, however, is computationally expensive, so practical systems use efficient techniques based on a particular three-valued logic, although this often leads to

In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E , we introduce E -valued non-deterministic Turing machines (E NTMs) and E -valued deterministic Turing machines (E DTMs). We discuss different E valued recursively enumerable languages from width-first and depth-first recognition. We find that width-first recog...

The parametric shape analysis framework of Sagiv, Reps, and Wilhelm [45,46] uses three-valued structures as dataflow lattice elements to represent sets of states at different program points. The recent work of Yorsh, Reps, Sagiv, Wilhelm [48, 50] introduces a family of formulas in (classical, two-valued) logic that are isomorphic to three-valued structures [46] and represent the same sets of co...

In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general n-symbol or numerical valued refined neutro...

The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic p...

We introduce probabilistic many-valued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic many-valued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are P-complete for classical logic programs are shown to be co-NP-complete for probabilistic many-v...

Ontologies describe a conceptualization of a part of the world relevant to some application. What are the units of conceptualizations? Current ontologies often equate concepts with words from natural languages. Words are certainly not the smallest units of conceptualization, neither are the sets of synonyms of WordNet or other linguistically justified units. I suggest to take distinctions as ba...

In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P. -D. Février’s ’logic of complementarity’ as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is...

Choices in business processes are often based on the process history saved as a log-file listing events and their time stamps. In this paper we introduce a finite-path variant of the timed propositional logics with past for specifying guards in business process models. The novelty is due to the introduction of boundary points start and now corresponding to the starting and current observation p...