of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest

show in detail that H(#; @) is modally natural. We begin by studying its expressivity, and provide model theoretic characterizations (via a restricted notion of Ehrenfeucht-Frasse game, and an enriched notion of bisimulation) and a syntactic characterization (in terms of bounded formulas). The key

be characterized using formulas in first-order logic with transitive closure. We also define a non-standard (“supervaluational”) semantics for 3-valued first-order logic that is more precise than a conventional 3-valued semantics, and demonstrate that it can be effectively implemented using existing theorem

Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations

Bounded arithmetic is a branch of mathematical logic which characterize various classes of computational complexity by fragments of arithmetical theories. On the other hand, descriptive complexity gives another logical method to characterize complexity classes. However, until recently, no ac-

Introduction Prior to 1974, results in finite model theory had appeared only sporadically, e.g., Trakhtenbrot's Theorem [74] and the 0-1 law for first-order logic [23]: there had been no real concerted research effort. The main reason for this lack of development was that many

Abstract not found

We give some sufficient conditions under which any valued field that admits quantifier elimination in the Macintyre language is henselian. Then, without extra assumptions, we prove that if a valued field of characteristic (0, 0) has a Z-group as its value group and admits quantifier elimination in the main sort of the Denef-Pas style language LRRP then it is henselian. In fact the proof of this suggests that a quite large class of Denef-Pas style languages is natural with respect to henselianity.

Abstract not found

A proof-theoretic characterization of logical languages that form suitable bases for Prolog-like programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide