With the increasing empirical success of distributional models of compositional semantics, it is timely to consider the types of textual logic that such models are capable of capturing. In this paper, we address shortcomings in the ability of current models to capture logical operations such as negation. As a solution we propose a tripartite formulation for a continuous vector space representat...

Prolog is originally rooted in logic with the elegant mapping: “programs = formulas, execution = proof search”. Constraint logic programming extends Prolog to program in a richer structure than mere Herbrand terms. The underlying constraint solving engine requires either to be built-in or to add coroutines mechanisms that are not in the scope of logical reading. Implementations add other non-lo...

Sieber has described a model of PCF consisting of continuous functions that are invariant under certain ((nitary) logical relations, and shown that it is fully abstract for closed terms of up to third-order types. We show that one may achieve full abstraction at all types using a form of \Kripke logical relations" introduced by Jung and Tiuryn to characterize-deenability.

Dependency-based Compositional Semantics (DCS) provides a precise and expressive way to model semantics of natural language queries on relational databases, by simple dependency-like trees. Recently abstract denotation is proposed to enable generic logical inference on DCS. In this paper, we discuss some other possibilities to equip DCS with logical inference, and we discuss further on how logi...

The papers in this collection are all devoted to single theme: logic and its applications in computational linguistics. They share many themes, goals and techniques, and any editorial classification is bound to highlight some connections at the expense of other. Nonetheless, we have found it useful to divide these papers (somewhat arbitrarily) into the following four categories: logical semanti...

In this paper, we study the impact of two notions of core on the output of ranking semantics in logical argumentation frameworks. We consider the existential rules fragment, a language widely used in Semantic Web and Ontology Based Data Access applications. Using burden semantics as example we show how some ranking semantics yield different outputs on the argumentation graph and its cores. We e...

This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and algorithms currently used in natural language semantics, defined as the mapping of a statement to logical formulas — formulas, because a statement can be ambiguous...