相关论文: Typed Hilbert Epsilon Operators and the Semantics …
Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert's epsilon-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the epsilon-operator underspecified.…
The variation of word meaning according to the context leads us to enrich the type system of our syntactical and semantic analyser of French based on categorial grammars and Montague semantics (or lambda-DRT). The main advantage of a deep…
This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for…
This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical…
We propose a cognitively and linguistically motivated set of sorts for lexical semantics in a compositional setting: the classifiers in languages that do have such pronouns. These sorts are needed to include lexical considerations in a…
Free variables occur frequently in mathematics and computer science with ad hoc and altering semantics. We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…
We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a…
We investigate the elimination of quantifiers in first-order formulas via Hilbert's epsilon-operator (or -binder), following Bernays' explicit definitions of the existential and the universal quantifier symbol by means of epsilon-terms.…
Previous work on English determiners has primarily concentrated on their semantics or scoping properties rather than their complex ordering behavior. The little work that has been done on determiner ordering generally splits determiners…
This paper proposes to compute the meanings associated to sentences with generic NPs corresponding to the most of generalized quantifier. We call these generics specimens and they resemble stereotypes or prototypes in lexical semantics. The…
We present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many sorted higher order logic. Word meaning is depicted by lambda terms of second order lambda…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and…
We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing "algebraic" semantics for nonclassical first-order logics. This framework includes a natural notion of substitution, which allows…
Two types of explanations have been receiving increased attention in the literature when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
Possessive pronouns are used as determiners in English when no equivalent would be used in a Japanese sentence with the same meaning. This paper proposes a heuristic method of generating such possessive pronouns even when there is no…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…