All promiment examples of first-order predicate fuzzy logics are undecidable. This leads to the problem of the arithmetical complexity of their sets of tautologies and satisfiable sentences. This paper is a contribution to the general study of this problem. We propose the classes of first-order core and ∆-core fuzzy logics as a good framework to address these arithmetical complexity issues. We ...

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

Quantification theory, or first-order predicate logic, can be formulated in terms purely of predicate letters and a few predicate functors which attach t o predicates to form further predicates. Apart from the predicate letters, which are schematic, there are no variables. On this score the plan is reminiscent of the combinatory logic of Schonfinkel and Curry. Theirs, however, had the whole of ...

Using the framework of artificial chemistries (ACs) an automated theorem prover (ATP) is constructed. Though it is an application of its own, in the context of ACs automated theorem proving can serve a second purpose. In this paper, we present a resolution-based AC named RESAC. Once converted to the first-order predicate calculus a problem straightly fits to this non-deterministic AC model. The...

We present a selective backtracking method for Horn clause programs, as applied to Prolog (2)[8)(11)[12], a programming language based on first-order predicate calculus (3)(4)~ developed at the university of Marseille (18]. This method is based on the general method expounded in (7] for backtracking intelligently in AND/OR trees. It consists, essentially, in avoiding backtracking to any goal wh...