In this paper, we characterize the logical consequence relation as the minimal relation in a class of 'adequate consequence relations for quantification theory. These adequate relations are easily seen to include the usual syntactic relations of deductive consequence and thus our results can, perhaps, be considered an abstract version of the completeness theorem. Our work is closely related to ...

A first-order sentence θ of vocabulary σ ∪ {S} is successor-invariant in the finite if for every finite σ-structure M and successor relations S1 and S2 on M, (M, S1) |= θ ⇐⇒ (M, S2) |= θ. In this paper I give an example of a non-first-order definable class of finite structures which is, however, defined by a successor-invariant first-order sentence. This strengthens a corresponding result for o...

In this paper we define computationally well-behaved versions of classical first-order logic and prove that the validity problem is decidable1.

I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are...

We consider successor-invariant first-order logic (FO+ succ)inv, consisting of sentences Φ involving an “auxiliary” binary relation S such that (A, S1) |= Φ ⇐⇒ (A, S2) |= Φ for all finite structures A and successor relations S1, S2 on A. A successorinvariant sentence Φ has a well-defined semantics on finite structures A with no given successor relation: one simply evaluates Φ on (A, S) for an a...

We prove that for the class of sets of words indexed by countable scattered linear orderings, there is an equivalence between definability in first-order logic, star-free expressions with marked product, and recognizability by finite aperiodic semigroups which satisfy the equation xωx−ω = x. 1998 ACM Subject Classification F.4.1 Mathematical Logic; F.4.3 Formal Languages

Mathematical models described by multivariable functions f(x ) where x 1⁄4 ðx1;...; xnÞ are investigated. If the model output is influenced mainly by low order combinations of input variables x1;...; xn; an attempt can be made to construct a low order approximation to the model using values of f(x ) only. q 2002 Elsevier Science Ltd. All rights reserved.