In general, first-order predicate logic extended with linear integer arithmetic is undecidable. We show that the Bernays–Schönfinkel–Ramsey fragment (∃∗∀∗-sentences) extended with a restricted form of linear integer arithmetic is decidable via finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures cons...

An indexing technique for first-order predicate logic terms and literals is proposed. It exploits the lattice structure of terms, generated by the usual instance relation, to provide for a given “query term” fast access to all T-unifiable terms, T-instances (backward subsumption) and T-generalized terms (forward subsumption) where T is any finitary unification theory. In the best case one singl...

Intuitionistic logic consists of the principles of reasoning which were used informally by L. E. J. Brouwer, formalized by A. Heyting (also partially by V. Glivenko), interpreted by A. Kolmogorov, and studied by G. Gentzen and K. Gödel during the first third of the twentieth century. Formally, intuitionistic first-order predicate logic is a proper subsystem of classical logic, obtained by repla...

A method to represent first-order predicate logic (Horn clause logic) by a data-flow network is presented. Like a data-flow computer for a von Neumann program, the proposed network explicitly represents the logical structure of a declarative program by unlabeled edges and operation nodes. In the deduction, the network first propagates symbolic tokens to create an expanded AND/OR network by the ...

We study the first-order model checking problem on two generalisations of pushdown graphs. The first class is the class of nested pushdown trees. The other is the class of collapsible pushdown graphs. Our main results are the following. First-order logic with reachability is uniformly decidable on nested pushdown trees. Considering first-order logic without reachability, we prove decidability i...