Related papers: Type-theoretical natural language semantics: on th…
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…
Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…
System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be (explicitly) instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction.…
We developed a type-theoretical framework for natural lan- guage semantics that, in addition to the usual Montagovian treatment of compositional semantics, includes a treatment of some phenomena of lex- ical semantic: coercions, meaning,…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
We reformulate recent advances in directed type theory--a type theory where the types have the structure of synthetic (higher) categories--as a logical calculus with multiple context 'zones', following the example of Pfenning and Davies.…
In a previous paper (of which this is a prosecution) we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended…
A coercion semantics of a programming language with subtyping is typically defined on typing derivations rather than on typing judgments. To avoid semantic ambiguity, such a semantics is expected to be coherent, i.e., independent of the…
Most categorical models for dependent types have traditionally been heavily set based: contexts form a category, and for each we have a set of types in said context -- and for each type a set of terms of said type. This is the case for…
In this paper, an application of automated theorem proving techniques to computational semantics is considered. In order to compute the presuppositions of a natural language discourse, several inference tasks arise. Instead of treating…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
The dependently-typed lambda calculus LF is often used as a vehicle for formalizing rule-based descriptions of object systems. Proving properties of object systems encoded in this fashion requires reasoning about formulas over LF typing…
Semantic type mismatch between a noun and its context is central to coercion phenomena. This paper introduces a graph-based method to examine how lexical and contextual type information is reflected in word embeddings. We select nouns from…
Lexical semantic typology has identified important cross-linguistic generalizations about the variation and commonalities in polysemy patterns---how languages package up meanings into words. Recent computational research has enabled…
Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration…
In recent work we have shown how it is possible to define very precise type systems for object-oriented languages by abstractly compiling a program into a Horn formula f. Then type inference amounts to resolving a certain goal w.r.t. the…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…