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 assertions about reachability in games of imperfect information against Nature. We then capitalize on this intuition by developing expressively equivalent (...) variants of dependence logic in which this interpretation is taken to the foreground. (shrink)

IFG logic is a variant of the independence-friendly logic of Hintikka and Sandu. We answer the question: “Which IFG-formulas are equivalent to ordinary first-order formulas?” We use the answer to prove the ordinary cylindric set algebra over a structure can be embedded into a reduct of the IFG-cylindric set algebra over the structure.

Independence Friendly Logic, introduced by Hintikka, is a logic in which a quantifier can be marked for being independent of other quantifiers. Dependence logic, introduced by Väänänen, is a logic with the complementary approach: for a quantifier it can be indicated on which quantifiers it depends. These logics are claimed to be useful for many phenomena, for instance natural language semantics. In this contribution we will compare these two logics by investigating their application in a compositional analysis of the de (...) dicto - de re ambiguity in natural language. It will be argued that Independence Friendly logic is suitable, whereas Dependence Logic is not. (shrink)

A dichotomy result of Sevenster (2014) [29] completely classified the quantifier prefixes of regular Independence-Friendly (IF) logic according to the patterns of quantifier dependence they contain. On one hand, prefixes that contain “Henkin” or “signalling” patterns were shown to characterize fragments of IF logic that capture NP-complete problems; all the remaining prefixes were shown instead to be essentially first-order. In the present paper we develop the machinery which is needed in order to extend the results of Sevenster to non-prenex, regular (...) IF sentences. This involves shifting attention from quantifier prefixes to a (rather general) class of syntactical tree prefixes. We partially classify the fragments of regular IF logic that are thus determined by syntactical trees; in particular, a) we identify four classes of tree prefixes that are neither signaling nor Henkin, and yet express NP-complete problems and other second-order concepts; and b) we give more general criteria for checking the first-orderness of an IF sentence. (shrink)

In this article we investigate the family of independence-friendly (IF) logics in the equality-free setting, concentrating on questions related to expressive power. Various natural equality-free fragments of logics in this family translate into existential second-order logic with prenex quantification of function symbols only and with the first-order parts of formulae equality-free. We study this fragment of existential second-order logic. Our principal technical result is that over finite models with a vocabulary consisting of unary relation symbols only, this fragment of second-order (...) logic is weaker in expressive power than first-order logic (with equality). Results about the fragment could turn out useful for example in the study of independence-friendly modal logics. In addition to proving results of a technical nature, we address issues related to a perspective from which IF logic is regarded as a specification framework for games, and also discuss the general significance of understanding fragments of second-order logic in investigations related to non-classical logics. (shrink)