First-order logic (FOL) is undecidable — that is, no algorithm exists that can decide whether a formula of FOL is valid or not. However, there are various fragments of FOL that are known to be decidable. FO, the two-variable fragment of FOL, is one of such languages [1, 2]. FO is a first-order language where formulas have maximally two variables, no function symbols, but possibly do have equali...

First-order logic (FOL) is undecidable — that is, no algorithm exists that can decide whether a formula of FOL is valid or not. However, there are various fragments of FOL that are known to be decidable. FO, the two-variable fragment of FOL, is one of such languages [1,2]. FO is a first-order language where formulas have maximally two variables, no function symbols, but possibly do have equalit...

Large systems are built from smaller parts. We present a method for deducing properties of a system by reasoning about its components. We show how to represent an individual component Πi by a formula Si so that the parallel composition usually denoted cobegin Π1 ‖ . . . ‖Πn coend is represented by the formula S1 ∧ . . . ∧ Sn. Composition is conjunction. We reduce composition to conjunction not ...

A language over an alphabet [Formula: see text] of opening ([Formula: text]) and closing brackets, is balanced if it a subset the Dyck text], well-formed all words are prefixes in text]. We show that well-formedness context-free decidable polynomial time, longest common reduced suffix can be computed time. With this at hand we decide for class 2-[Formula: non-linear tree transducers with output...

Introducing attentional mechanism in neural network is a powerful concept, and has achieved impressive results in many natural language processing tasks. However, most of the existing models impose attentional distribution on a flat topology, namely the entire input representation sequence. Clearly, any well-formed sentence has its accompanying syntactic tree structure, which is a much rich top...

This paper describes how ontologies are used to mediate between languages and to infer answers to user questions in the multilingual e-commerce mediation system mkbeem. As an example, the paper discusses how a complex user request in human language is transformed into an ontological formula and subsequently exploited to identify a service which matches best. The mkbeem-system prototype is in pr...

Computational Linguistics and Logic Programming have strong connections , but the former uses concepts that are absent from the most familiar implementations of the latter. We advocate that a Logic Programming language need not feature the Computational Linguistics concepts exactly, it must only provide a logical way of dealing with them. We focus on the manipulation of higher-order terms and t...

We investigate the quantifier alternation hierarchy of first-order logic over finite words. To do so, we rely on the separation problem. For each level in the hierarchy, this problem takes two regular languages as input and asks whether there exists a formula of the level that accepts all words in the first language and no word in the second one. Usually, obtaining an algorithm that solves this...