Non-classical logicians have significantly expanded the traditional field of using logical methods. The first them was three-digit logic Y. Lukasevich. Next came A. Bochvar, "quantum logics" G. Reichenbach and P. Detush-Fevrier, infinite-valued, probabilistic other logics. possibilities non-classical logics become widely used in various branches scientific knowledge. Polysemantic, fuzzy, intuit...

We show that the ideal sets of an argumentation framework can be characterized by two kinds of logical models: ideal models (2-valued logical models) and p-stable models (2-valued logical models). We also show that the maximal ideal set of an argumentation framework can be characterized by the well-founded+ model (a 3-valued logical model). These results argue for the logical foundations of the...

Fuzzy answer set programming [Saad, 2010; Saad, 2009; Subrahmanian, 1994] is a declarative framework for representing and reasoning about knowledge in fuzzy environments. However, the unavailability of fuzzy aggregates in disjunctive fuzzy logic programs, DFLP, with fuzzy answer set semantics [Saad, 2010] prohibits the natural and concise representation of many interesting problems. In this pap...

Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of...

This paper proposes an application of programming environments generation to structured document manipulation. We use the Centaur system as a formal tool to model and implement logical and physical document structure, logical structure editing, layout processing, format conversion, and document queries, for a sample class of documents: scientiic articles including equations and gures. We suppor...

Mathematical Fuzzy Logics [51,60] have a long tradition with roots going back to the many-valued logics of Łukasiewicz, Gödel, and Kleene [57, 68, 73] and the Fuzzy Set Theory of Zadeh [111]. Their purpose is to model vagueness or imprecision in the real world, by introducing new degrees of truth as additional shades of gray between the Boolean true and false. For example, one can express the d...

This paper introduces a new method of empowering Logical Petri Nets (LPN) and Fuzzy Logical Petri Nets (FLPN) [1] using multiple logic. In this paper we proposed a Multi-Logical Petri Nets (MLPN) and Multi-Logical Fuzzy Petri Nets (MLFPN) based on Logical Petri Nets (LPN) and Fuzzy Logical Petri Nets (FLPN). Here we have showed that, how multiple logic is implemented in MLPN and MLFPN. The prop...

We present a logical framework to represent and reason about fuzzy optimization problems based on fuzzy answer set optimization programming. This is accomplished by allowing fuzzy optimization aggregates, e.g., minimum and maximum in the language of fuzzy answer set optimization programming to allow minimization or maximization of some desired criteria under fuzzy environments. We show the appl...