Related papers: On the dependent conjunction and implication
Association Rules are a basic concept of data mining. They are, however, not understood as logical objects which can be used for reasoning. The purpose of this paper is to investigate a model based semantic for implications with certain…
The postulates of comprehension and extensionality in set theory are based on an inversion principle connecting set-theoretic abstraction and the property of having a member. An exactly analogous inversion principle connects functional…
Representing a word by its co-occurrences with other words in context is an effective way to capture the meaning of the word. However, the theory behind remains a challenge. In this work, taking the example of a word classification task, we…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory $T$ has enough structure, then the category $T\text{-}\mathbf{Mod}$ of its models carries the structure of a model…
The relationship between Lexical-Functional Grammar (LFG) {\em functional structures} (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that correctly explains…
We propose a system for the interpretation of anaphoric relationships between unbound pronouns and quantifiers. The main technical contribution of our proposal consists in combining generalized quantifiers with dependent types. Empirically,…
In this paper, we provide more evidence for the contention that logical consequence should be understood in normative terms. Hartry Field and John MacFarlane covered the classical case. We extend their work, examining what it means for an…
We investigate the possibility of distinguishing among different causal relations starting from a limited set of marginals. Our main tool is the notion of adhesivity, that is, the extension of probability or entropies defined only on…
Dependency syntax represents the structure of a sentence as a tree composed of dependencies, i.e., directed relations between lexical units. While in its more general form any such tree is allowed, in practice many are not plausible or are…
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
A copula of continuous random variables $X$ and $Y$ is called an \emph{implicit dependence copula} if there exist functions $\alpha$ and $\beta$ such that $\alpha(X) = \beta(Y)$ almost surely, which is equivalent to $C$ being factorizable…
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
This report is an extension of 'A Model of Parametric Dependent Type Theory in Bridge/Path Cubical Sets' (Nuyts, arXiv:1706.04383). The purpose of this text is to prove all technical aspects of our model for dependent type theory with…
We provide a wide-ranging study of the scenario where a subset of the relations in a relational vocabulary are visible to a user --- that is, their complete contents are known --- while the remaining relations are invisible. We also have a…
We introduce dependent adders. A dependent adder $A$ has for every $x \in A$ a way of adding together $x$ many elements of $A$. We provide examples from many disparate branches of mathematics. Examples include the field with one element…
In this paper, we show that \phi is a dependent formula if and only if all \phi-types have an extension to a \phi-isolated \phi-type that is an "elementary \phi-extension" (see Definition 2.3 in the paper). Moreover, we show that the domain…