We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures a semantic construction. After discussing some potential criteria, we focus on the criteri...

Non-Axiomatic Logic (NAL) is designed for intelligent reasoning, and can be used in a system that has insufficient knowledge and resources with respect to the problems to be solved. This paper reports the result of a case study that applies NAL in medical diagnostics, and the logic is compared with binary logic and probability theory.

This paper takes an axiomatic and calculational view of diversity (or “Nversion programming”), where multiple implementations of the same specification are executed in parallel to increase dependability. The central notion is “adjudication”: once we have multiple, potential different, outcomes, how do we come to a single result? Adjudication operators are explicitly defined and some general pro...

We consider an axiomatic characterization of the plurality rule, which selects the alternative(s) most preferred by the largest number of individuals. We strengthen the characterization result of Yeh (Economic Theory 34: 575–583, 2008) by replacing efficiency axiom by the weaker axiom called faithfulness. Formally, we show that the plurality rule is the only rule satisfying anonymity, neutralit...

In this paper, we show that the methods of mathematical statistical physics can be successfully applied to random fields in finite volumes. As a result, obtain simple necessary and sufficient conditions for existence uniqueness field with given system one-point conditional distributions. Using axiomatic (without notion potential) definition Hamiltonian, any is Gibbsian. We also apply proposed a...