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).

The multi-axiom grammars (MAG) are alternatives to the single-axiom context free grammars (CFG) and all-axiom algebraic grammars (AG) for programming language speci cation. Neither phrase recognition nor algebraic mechanisms for language processing are supported by CFGs. AGs support algebraic mechanisms for language processing but specify a smaller class of languages. MAGs avoid these limitatio...

If someone claims that individuals behave as if they violate the independence axiom when making decisions over simple lotteries, it is invariably on the basis of experiments and theories that must assume the independence axiom through the use of the random lottery incentive mechanism. We refer to someone who holds this view as a Bipolar Behaviorist, exhibiting pessimism about the axiom when it ...