In the present paper, we introduce the fuzzy Nehring axiom, fuzzy Sen axiom and weaker form of the weak fuzzycongruence axiom. We establish interrelations between these axioms and their relation with fuzzy Chernoff axiom. Weexpress full rationality of a fuzzy choice function using these axioms along with the fuzzy Chernoff axiom.

In this paper it is studied the role of the axiom of choice in some theorems in which the concepts of first and second countability are used. Results such as the following are established: (1) In ZF (Zermelo–Fraenkel set theory without the axiom of choice), equivalent are: (i) every base of a second countable space has a countable subfamily which is a base; (ii) the axiom of countable choice fo...

We show that the Dushnik-Miller Theorem for countable linear order-ings (stating that any countable linear ordering has a nontrivial self-embedding) is equivalent (over recursive comprehension (RCA 0)) to arithmetic comprehension (ACA 0). This paper presents a result in reverse mathematics, a program initiated by H. Friedman and S. Simpson, trying to determine the weakest possible \set-theoreti...

Absorptions are generally employed in Description Logics (DL) reasoners in a uniform way regardless of the structure of an input knowledge base. In this paper we present an approach to encode some state-of-the-art absorption techniques into a state space planner, aiming to achieve a better solution. The planner applies appropriate operators to general axioms and produces a solution with a minim...

Tony Martin proved in [Mar98] that the Axiom of Determinacy AD implies the Axiom of Blackwell Determinacy Bl-AD, and conjectured that the converse holds as well: Conjecture 1 The Axiom of Blackwell Determinacy Bl-AD implies the Axiom of Determinacy AD. Although Martin, Neeman and Vervoort in their [MarNeeVer03] have made considerable progress on Martin’s Conjecture 1, the full conjecture remain...

In the approximate fuzzy reasoning the covering over of fuzzy rule base input and rule premise of a rule determines the importance of that fuzzy rule and the rule output as well. An axiom system has been created, describing the relationship between the fuzzy rule base system, rule input and rule output. By using distance-based operators a novel reasoning method appears by the compositional rule...

Optimized Recovery (OR) adds belief base optimization to the traditional Recovery postulate—improving Recovery adherence without sacrificing adherence to the more accepted postulates or to the foundations approach. Reconsideration and belief liberation systems both optimize a knowledge base through consolidation of a chain of base beliefs; and recovered base beliefs are returned to the base. Th...

philosophers from one hand take the “al-vahed” axiom for granted, and on the other hand, they assume that the almighty to be of absolute power. now the question is whether: this is at odds with the “al- vahed” axiom? how can we accept at the same time the absolute power of the almighty and the “al-vahed” axiom? we should say here: majority of philosophers, mystics and kalam specialists have cla...

26 2. 1 is not a proof. From the induction hypotheses we have that`MT 1 = fail. If s 0 is either an axiom or an assumption, then is apply(then(t 1 ; \t "); \s 0 ") and`MT Tac(\s 0 "). If s 0 is neither an axiom nor an assumption, then is apply(then(t 1 ; \t "); fail) with`MT Tac(fail). In both cases, from axiom (A9), the induction hypotheses and by applying ifE we havè MT = fail 25 Theorem C.1 ...