In this paper, we discuss the semantics of disjunctive programs and databases and show how multivalued mappings and their fixed points arise naturally within this context. A number of fixed-point theorems for multivalued mappings are considered, some of which are already known and some of which are new. The notion of a normal derivative of a disjunctive program is introduced. Normal derivatives...

One of the most used assumptions in logic programming and deductive databases is the so-called Closed World Assumption (CWA), according to which the atoms that cannot be inferred from the programs are considered to be false (i.e. a pessimistic assumption). One of the most successful semantics of conventional logic programs based on the CWA is the well-founded semantics. However, the CWA is not ...

We present introductory considerations and analysis toward computing applications based on the recently introduced deterministic logic scheme with random spike (pulse) trains [Phys. Lett. A 373 (2009) 2338–2342]. Also, in considering the questions, “why random?” and “why pulses?”, we show that the random pulse based scheme provides the advantages of realizing multivalued deterministic logic. Pu...

In the present paper‎, ‎we introduce the concept of generalized multivalued $F$ -‎contraction mappings and give a fixed point result‎, ‎which is a proper‎ ‎generalization of some multivalued fixed point theorems including Nadler's‎.

If we view fuzzy logic as a logic, i.e., as a particular case of a multivalued logic, then one of the most natural questions to ask is whether the corresponding propositional logic is decidable, i.e., does there exist an algorithm that, given two propositional formulas F and G, decides whether these two formulas always have the same truth value. It is known that the simplest fuzzy logic, in whi...

The main aim of this paper is to create a general Truth Maintenance System based on the De Kleer 5] algorithm. This kind of system is to be designed so that it can be used in diierent propositional monotonic logic models of reasoning systems. The knowledge base system that will interact with it is described. Furthermore, we study the eeciency that transferring ATMS to a logic with several truth...

We describe the embedding of the semantic notions and modal operators of a fir st-order temporal logic based on time intervals in a multivalued setting. Truth values will be realized as functions from time intervals to "ordinary" truth values like t and f . The main emphasis lies on the realization of the various modal operators contained in the temporal logic as operations on the functional tr...

We propose a technique for dealing with the high complexity of reasoning under propositional default logic and circumscription. The technique is based on the notion of approximation: A logical consequence relation is computed by means of sound and progressively \more complete" relations, as well as complete and progressively \more sound" ones. Both sequences generated in this way converge to th...

A program called MVSIS has been developed which optimizes multi-level multi-valued networks (MV networks). We describe what such a network is and the capabilities contained in MVSIS. MVSIS is modeled after SIS, which synthesizes binary multi-level networks, but the logic network of MVSIS is such that all variables can be multivalued each with its own range. Included in MVSIS are almost all the ...