Ordered Completion for First-Order Logic Programs on Finite Structures

Embedded Finite Models, Stability Theory and the Impact of Order

We extend bounds on the expressive power of firstorder logic over finite structures and over ordered finite structures, by generalizing to the situation where the finite structures are embedded in an infinite structure M , where M satisfies some simple combinatorial properties studied in model-theoretic stability theory. We first consider first-order logic over finite structures embedded in a s...

Logic Programs with Ordered Disjunction: First-Order Semantics and Expressiveness

Logic programs with ordered disjunction (LPODs) (Brewka 2002) generalize normal logic programs by combining alternative and ranked options in the heads of rules. It has been showed that LPODs are useful in a number of areas including game theory, policy languages, planning and argumentations. In this paper, we extend propositional LPODs to the first-order case, where a classical second-order fo...

First-Order Logic vs. Fixed-Point Logic in Finite Set Theory

The ordered conjecture states that least fixed-point logic LFP is strictly more expressive than first-order logic FO on every infinite class of ordered finite structures. It has been established that either way of settling this conjecture would resolve open problems in complexity theory. In fact, this holds true even for the particular instance of the ordered conjecture on the class of BIT-stru...

Two-Variable Logic on 2-Dimensional Structures

This paper continues the study of the two-variable fragment of first-order logic (FO2) over twodimensional structures, more precisely structures with two orders, their induced successor relations and arbitrarily many unary relations. Our main focus is on ordered data words which are finite sequences from the set Σ×D where Σ is a finite alphabet and D is an ordered domain. These are naturally re...

Number of Variables and Expressive Power of First-Order Logic on Finite Ordered Structures