In this paper, we propose a translation from normal first-order logic programs under the answer set semantics to first-order theories on finite structures. Specifically, we introduce ordered completions which are modifications of Clark’s completions with some extra predicates added to keep track of the derivation order, and show that on finite structures, classical models of the ordered-complet...

We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even if we allow ε-contractions and reachability predicates (with regular constraints) for pairs of configurations, the structures remain tree-automatic whence their first-order logic theories are decidable. As a corollary we obtain the tree-automaticity of the second level of the Caucal-hierarchy.

SAT is not in P is proved, in a first-order theory, with a new single finite axiom of Turing’s theory of computing. So, P is not equal to NP.

In this paper, we examine the divide between stable and unstable first-order theories in model theory. We begin by defining a stable theory and proving Shelah’s theorem, which reduces the question of stability to a problem of examining a single formula. Afterwards, we will provide some applications of the stability/instability divide to other model-theoretic questions, such as the question of c...

James Ax showed that, in each characteristic, there is a natural bijection from the space of complete theories of pseudo-finite fields, in first order logic, to the set of conjugacy classes of procyclic subgroups of the absolute Galois group of the prime field. I show that when the set of subgroups of a profinite group is considered to have the Vietoris (a.k.a. hyperspace, finite, exponential, ...

Voids are extremely important to water science, because their size and connectivity determines the storage and flow of water both above and below the ground surface. While previous formal theories about voids strictly consider holes hosted inside objects, we generalize voids to also include spaces between objects, and distinguish voids in macroscopic objects from those occurring microscopically...

Probability Estimation Trees (PETs) [9] try to estimate the probability with which an instance belongs to a certain class, rather than just predicting its most likely class. Several approaches for learning PETs have been proposed, mainly in a propositional context. Since we are interested in applying PETs in a relational context, we make some simple modifications to the first-order tree learner...

The Fluent Calculus belongs to the established predicate calculus formalisms for reasoning about actions. Its underlying concept of state update axioms provides a solution to the basic representational and inferential Frame Problems in pure first-order logic. Extending a recent research result, we present a Fluent Calculus to reason about domains involving continuous change and where actions oc...

We present a formalisation for the notion of viewpoint, a construct meant for expressing several varieties of relativised truth. The formalisation consists in a logic which extends rst order predicate calculus through an axiomatization of provability and with the addition of proper reeection rules. The extension is not conservative, but consistency is granted. Viewpoints are deened as set of re...

We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which nominal rewriting provides a complete procedure to check nominal algebra equality. This subclass includes specifications of lambda-calculus and first-order ...