4 Axioms of ZFC 7 4.1 Axiom of extensionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 Axiom of the empty set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3 Axiom of unordered pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.4 Axiom of union . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.5 Axiom of infinity . . ...

In this paper, we present a hypergraph-based inference method for conditional independence. Our method allows us to obtain several interesting results on graph combination. In particular, our hypergraph approach allows us to strengthen one result obtained in a conventional graph-based approach. We also introduce a new inference axiom, called combination, of which the contraction axiom is a spec...

1 Three Axioms for a Determinant Function Let d be a scalar-valued function on the space Mn×n of all n×n matrices. Let A1, A2, . . . , An be the n rows of an n×n matrix A. We will denote the value d(A) of A under the function d as d(A) = d(A1, A2, . . . , An), indicating that d is a scalar-valued function of n n-dimensional row vectors A1, A2, . . . , An. The scalar-valued function d is called ...

This paper presents the design and implementation of a real-time fuzzy-based artificial intelligence system for an interactive game. The chosen game is a remake of Pac-Man in which the opponents are BDI-style intelligent agents. The components of the system and the methods used in fuzzifying the game’s rules and variables are discussed. In addition, comparisons are drawn between the proposed fu...

We introduce the Bounded Axiom A Forcing Axiom(BAAFA). It turns out that it is equiconsistent with the existence of a regular Σ2-correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom(BPFA).

In this paper, we first extend the concept of arity in crisp convex spaces to case fuzzification and give some related properties. From view hull operator, study relations between disjoint sum M-fuzzifying its factor spaces. We also examine additivity degree separability (S0,S1,S2,S3,S4). Finally, show that every space is JHC iff corresponding JHC.