Incorporating the Basic Elements of a First-degree Fuzzy Logic and Certain Elments of Temporal Logic for Dynamic Management Applications

The approximate reasoning is perceived as a derivation of new formulas with the corresponding temporal attributes, within a fuzzy theory defined by the fuzzy set of special axioms. For dynamic management applications, the reasoning is evolutionary because of unexpected events which may change the state of the expert system. In this kind of situations it is necessary to elaborate certain mechanisms in order to maintain the coherence of the obtained conclusions, to figure out their degree of reliability and the time domain for which these are true. These last aspects stand as possible further directions of development at a basic logic level. The purpose of this paper is to characterise an extended fuzzy logic system with modal operators, attained by incorporating the basic elements of a first-degree fuzzy logic and certain elements of temporal logic.Dynamic Management Applications, Fuzzy Reasoning, Formalization, Time Restrictions, Modal Operators, Real-Time Expert Decision System (RTEDS)

Toward a probability theory for product logic: states, integral representation and reasoning

The aim of this paper is to extend probability theory from the classical to the product t-norm fuzzy logic setting. More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called state, and show that every state is the Lebesgue integral with respect to a unique regular Borel probability measure. Furthermore, the relation between states and measures is shown to be one-one. In addition, we study geometrical properties of the convex set of states and show that extremal states, i.e., the extremal points of the state space, are the same as the truth-value assignments of the logic. Finally, we axiomatize a two-tiered modal logic for probabilistic reasoning on product logic events and prove soundness and completeness with respect to probabilistic spaces, where the algebra is a free product algebra and the measure is a state in the above sense.Comment: 27 pages, 1 figur

The Varieties of Ought-implies-Can and Deontic STIT Logic

STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings