The paper draws attention to an important, but apparently neglected distinction relating to axiomatic theories of truth, viz. the distinction between weakly and strongly truth-compositional theories of truth. The paper argues that the distinction might be helpful in classifying weak axiomatic theories of truth and examines some of them with respect to it.

This paper brings together some points made previously in (Sieg and Schlimm 2005) and (Sieg and Schlimm 2014) focusing on some aspects of Dedekind’s axiomatic approach to the foundations of mathematics. In particular the terminology for his axiomatic definitions of concepts and the development of the notion of mapping are discussed.

An axiomatic formulation of a logic called LPS4 appears in [3]. Here that logic is proved sound and complete with respect to the weak semantics of [7]. Also a tableau system for LPS4 is introduced, and also proved sound and complete with respect to the semantics, thus establishing both cut elimination and equivalence with the axiomatic formulation.

There are simple, purely syntactic axiomatic proof systems for both the logical truths and the logical falsehoods of propositional logic. However, to date no such system has been developed for the logical contingencies, that is, formulas that are both satisfiable and falsifiable. This paper formalizes and purely syntactic axiomatic proof systems for the logical contingencies and proves its soun...

This report summarizes a PhD research effort to implement a type of logic programming language called “axiomatic language”. Axiomatic language is intended as a specification language, so its implementation involves the transformation of specifications to efficient algorithms. The language is described and the implementation task is discussed. 1998 ACM Subject Classification D.1.6 Logic Programm...

In this paper, axiomatic testing of software metrics will be described, The testing is based on representation axiomsjfom the measurement theory. In a case study, the axioms are given for the formal relational structure and the empirical relational structure. 'livo approaches of axiomatic testing are elaborated: deterministic and probabilistic testing.

An axiomatic formulation of a logic called LPS4 appears in [3]. Here that logic is proved sound and complete with respect to the weak semantics of [7]. Also a tableau system for LPS4 is introduced, and also proved sound and complete with respect to the semantics, thus establishing both cut elimination and equivalence with the axiomatic formulation.

We are living in a world where complexity of systems created and studied by people grows beyond all imaginable limits. Computers, their software and their networks are among the most complicated systems of our time. Science is the only efficient tool for dealing with this overwhelming complexity. One of the methodologies developed in science is the axiomatic approach. It proved to be very power...

The concept of informational independence plays a key role in most knowledge-based systems. J. Pearl and his co-researchers have analysed the basic properties of the concept and have formulated an axiomatic system for informational independence. This axiomatic system focuses on independences among mutually disjoint sets of variables. We show that in the context of probabilistic independence a f...