Distributed representations (such as those based on embed-dings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We present a model theory/semantics for first order logic based on vectors of reals. We describe the model theory , discuss some interesting properties of such ...

This paper attempts to serve as an introduction to abstract model theory. We introduce the notion of abstract logics, explore first-order logic as an instance of and as the basis for abstract logics, and end by proving Lindström’s theorem.

Collection List

Axiomatizations of the General Theory of Relativity.have occasionally been conducted to achieve precision and clarification of underlying concepts. Rigorous and inspiring work towards that aim based on first-order logic has been performed by Professor Németi and his working group (see references below). A complementary approach (Benda 2008) constructs the relativistic spacetime manifold ab init...

Digitally collected data su↵ers from many data quality issues, such as duplicate, incorrect, or incomplete data. A common approach for counteracting these issues is to formulate a set of data cleaning rules to identify and repair incorrect, duplicate and missing data. Data cleaning systems must be able to treat data quality rules holistically, to incorporate heterogeneous constraints within a s...

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.