Dealing with uncertainty is a very important issue in description logics (DLs). In this paper, we present PrDL‐ Litebool N a new probabilistic extension of DL‐ Litebool N , known as a very expressive DL‐Lite, by supporting the belief degree interval in a single axiom or a set of axioms connected with conjunction (by ∧) or disjunction (by ∨) operators. The PrDL‐ Litebool N semantics is based on ...

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 ...

In the paper we formulate an axiom CPA prism, which is the most prominent version of the Covering Property Axiom CPA, and discuss several of its implications. In particular, we show that it implies that the following cardinal characteristics of continuum are equal to ω1, while c = ω2: the independence number i, the reaping number r, the almost disjoint number a, and the ultrafilter base number ...

The report outlines the derived syntax provided within the HP-SL specification language to enable the definition ofrecord and union types. It describes the notation at two levels. First it describes the requirements for such a not.ation by way of an example the informally defines the derived short-hand notation. Secondly it provides a det.ailed definition by way of axiom schemas of the translat...

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).

Logicians frequently use axiom schemata to encode (potentially infinite) sets of sentences with particular syntactic form. In this paper we examine a first-order language in which it is possible to write expressions that both describe sentences and assert the truth of the sentences so described. The effect of adding such expressions to a knowledge base is the same as directly including the set ...