We consider fragments of first-order logic over finite words. In particular, we deal with first-order logic with a restricted number of variables and with the lower levels of the alternation hierarchy. We use the algebraic approach to show decidability of expressibility within these fragments. As a byproduct, we survey several characterizations of the respective fragments. We give complete proo...

Craig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss some applications of our results to the theory of institutio...

In this paper we consider the partial many-sorted first-order logic and its extension to the subsorted partial many-sorted first-order logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not hold for these logics in general (i.e., with respect to arbitrary signature morphisms). Then we for...

We propose and analyse a new countermeasure against Differential Power Analysis (DPA) for the AES encryption algorithm, based on permutation tables. As opposed to existing AES countermeasures, it does not use random masking. We prove that our new countermeasure is resistant against first-order DPA; we also show that it is quite efficient in practice.

Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually dependent on that order relation. This is somewhat surprising since order-invariant properties are more of a combinatorial rather than a logical object. We provide ...

The Collatz problem is reformulated in three ways as a non-arithmetic problem in first-order logic.

The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method, and argue that non-deceptiveness i...

The generative conception of grammars relies on the derivation process which, to its turn, depends on a hierarchical representation of syntax. We show in this paper how a fully constraint-based approach, avoiding such restriction, can constitute an alternative to generativity and form the basis of a framework for a model-theoretic conception of grammar.

We rely on the strength of linguistic and philosophical perspectives in constructing a framework that offers a unified explanation for presuppositions and existential commitment. We use a rich ontology and a set of methodological principles that embed the essence of Meinong’s philosophy and Grice’s conversational principles into a stratified logic, under an unrestricted interpretation of the qu...

Business modelling methods are popular but, since they operate primarily in the early stages of software lifecycles, most are informal. This paper describes how we have used a conventional formal notation (first order predicate logic) in combination with automated support tools to replicate the key components of an established, informal, business modelling method: IBM’s Business System Developm...