Related papers: From compositional to systematic semantics
In this paper, I argue, contrary to the prevailing opinion in the linguistics and philosophy literature, that a sortal approach to aspectual composition can indeed be explanatory. In support of this view, I develop a synthesis of competing…
We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the…
Current approaches for the discovery, specification, and provision of services ignore the relationship between the service contract and the conditions in which the service can guarantee its contract. Moreover, they do not use formal methods…
Semantic subtyping is an approach to define subtyping relations for type systems featuring union and intersection type connectives. It has been studied only for strict languages, and it is unsound for non-strict semantics. In this work, we…
Compositionality, the phenomenon where the meaning of a phrase can be derived from its constituent parts, is a hallmark of human language. At the same time, many phrases are non-compositional, carrying a meaning beyond that of each part in…
Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
We extend the usual internal logic of a (pre)topos to a more general interpretation, called the stack semantics, which allows for "unbounded" quantifiers ranging over the class of objects of the topos. Using well-founded relations inside…
A formal theory based on a binary operator of directional associative relation is constructed in the article and an understanding of an associative normal form of image constructions is introduced. A model of a commutative semigroup, which…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations…
Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases it is not possible to assign a direct…
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
Different analytic notions of contextuality fall into two major groups: probabilistic and strong notions of contextuality. Kochen and Specker's Theorem~0 is a demarcation criterion for differentiating between those groups. Whereas…
Natural language allows us to refer to novel composite concepts by combining expressions denoting their parts according to systematic rules, a property known as \emph{compositionality}. In this paper, we study whether the language emerging…
The foundational concepts of semantic numeration systems theory are briefly outlined. The action of cardinal semantic operators unfolds over a set of cardinal abstract entities belonging to the cardinal semantic multeity. The cardinal…
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by…
The central focus is on clarifying the distinction between sets and proper classes. To this end we identify several categories of concepts (surveyable, definite, indefinite), and we attribute the classical set theoretic paradoxes to a…
Identifying the relations that exist between words (or entities) is important for various natural language processing tasks such as, relational search, noun-modifier classification and analogy detection. A popular approach to represent the…