We examine the relationship between Dependence Logic and game logics. A variant of Dynamic Game Logic, called Transition Logic, is developed, and we show that its relationship with Dependence Logic is comparable to the one between First-Order Logic and Dynamic Game Logic discussed by van Benthem. This suggests a new perspective on the interpretation of Dependence Logic formulas, in terms of ass...

Inquisitive first-order logic, InqBQ, extends classical first-order logic with questions. From a technical perspective, InqBQ allows us to talk about a plurality of first-order structures, expressing not only facts about each structure in isolation, but also about how these structures relate to each other. We describe an Ehrenfeucht-Fräıssé game for InqBQ and show that this characterizes the ex...

Recent research in diagnosis (Mcllraith, 1997; Thielscher, 1997; McIlraith, 1998) extends earlier works in diagnosis fi’om first principles by using an action theory instead of a first-order theory to describe the correct behavior of the system in consideration. The action theory allows us to reason about actions and their effects. Thus, when an action does not yield the expected effects someth...

We establish some results on the Wadge degrees and on the Boolean hierarchy of k-partitions of some spaces, where k is a natural number. The main attention is paid to the Baire space, Baire domain and their close relatives. For the case of Δ2-measurable k-partitions the structures of Wadge degrees are characterized completely. For many degree structures, undecidability of the first-order theori...

A probability distribution can be given to the set of isomorphism classes of models with universe {1, . . . , n} of a sentence (i.e. closed formula) in first-order logic. We study the entropy of this distribution and derive a result from the 0-1 law for first-order sentences.

1 Logic 2 1.1 Aristotelean logic . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Subjects and predicates . . . . . . . . . . . . . . . . . . . 3 1.1.2 Syllogisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 The predicate calculus . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Predicates and individuals . . . . . . . . . . . . . . . . . . 5 1.2.2 Formulas an...

We investigate expressiveness and definability issues with respect to minimal models, particularly in the scope of Circumscription. First, we give a proof of the failure of the Löwenheim-Skolem Theorem for Circumscription. Then we show that, if the class of P ;Z-minimal models of a first-order sentence is ∆elementary, then it is elementary. That is, whenever the circumscription of a firstorder ...

In recent years there has been a growing demand for Automated Theorem Proving (ATP) in large theories, which often have more axioms than can be handled effectively as normal internal axioms. This work addresses the issues of accessing external sources of axioms from a first-order logic ATP system, and presents an implemented ATP system that retrieves external axioms asynchronously, on demand.

We discuss the use of model building for temporal representations. We chose Polish to illustrate our discussion because it has an interesting aspectual system, but the points we wish to make are not language specific. Rather, our goal is to develop theoretical and computational tools for temporal model building tasks in computational semantics. To this end, we present a first-order theory of ti...

Logics for ‘generally’ are intended to express some vague notions, such as ‘generally’, ‘several’, ‘many’, ‘most’, etc., by means of the new generalized quantifier ∇ and to reason about assertions with ‘generally’ (important issues in qualitative reasoning). We introduce the idea of functional interpretation for ‘generally’ and show that representative functions (akin to Skolem functions) enabl...