Set Of First-order Axioms Research Articles

Axiomatic characterization of the interval function of partial cubes and partial Hamming graphs

Interval function of a graph is a well-known notion in metric graph theory and the axiomatic characterization using a set of first order axioms of different graph classes is an interesting problem in this area. Partial cubes and partial Hamming graphs form one of the central graph class that can be embedded into hypercubes and Hamming graphs respectively. In this paper we present an axiomatic characterization of the interval function of partial cubes and partial Hamming graphs, using different first order axioms. Further, we give an axiomatic characterization of the interval function of these graphs using axioms on an arbitrary function R on V.

On Program Completion, with an Application to the Sum and Product Puzzle

AbstractThis paper describes a generalization of Clark’s completion that is applicable to logic programs containing arithmetic operations and produces syntactically simple, natural looking formulas. If a set of first-order axioms is equivalent to the completion of a program, then we may be able to find standard models of these axioms by running an answer set solver. As an example, we apply this “reverse completion” procedure to the Sum and Product Puzzle.

Probabilistic characterisation of models of first-order theories

We study probabilistic characterisation of a random model of a finite set of first order axioms. Given a set of first order axioms T and a structure M which we only know is a model of T, we are interested in the probability that M would satisfy a sentence ψ. Answering this question for all sentences in the language will give a probability distribution over the set of sentences which can be regarded as the probabilistic characterisation of the model M. We investigate defining these probabilistic characterisations as the limit of probability functions imposed on the set of finite models of T. We show how a symmetry axiom can uniquely specify the probability function over finite models and will study the existence of the limit in terms of the quantifier complexity of T.

Linear Measurement Models—Axiomatizations and Axiomatizability

This paper examines, in the scope of representational measurement theory, different axiomatizations and axiomatizability of linear and bilinear representations of ordinal data contexts in real vector spaces. The representation theorems proved in this paper are modifications and generalizations of Scott's characterization of finite linear measurement models. The advantage of these representation theorems is that they use only finitely many axioms, the number of which depends on the size of the given ordinal data context. Concerning the axiomatizability, it is proved by model-theoretic methods that finite linear measurement models cannot be axiomatized by a finite set of first order axioms.