Related papers: Extensional concepts in intensional type theory, r…
A model of Martin-L\"of extensional type theory with universes is formalized in Agda, an interactive proof system based on Martin-L\"of intensional type theory. This may be understood, we claim, as a solution to the old problem of modelling…
We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.
Initial Semantics aims at interpreting the syntax associated to a signature as the initial object of some category of 'models', yielding induction and recursion principles for abstract syntax. Zsid\'o proves an initiality result for…
We give new estimates of lengths of extremal rays of birational type for toric varieties. We can see that our new estimates are the best by constructing some examples explicitly. As applications, we discuss the nefness and…
The definitional equality of an intensional type theory is its test of type compatibility. Today's systems rely on ordinary evaluation semantics to compare expressions in types, frustrating users with type errors arising when evaluation…
We show that the intuitionistic first-order theory of equality has continuum many complete extensions. We also study the Vitali equivalence relation and show there are many intuitionistically precise versions of it.
In this paper we propose a categorical theory of intensionality. We first revisit the notion of intensionality, and discuss we its relevance to logic and computer science. It turns out that 1-category theory is not the most appropriate…
We introduce a new model construction for Martin-L\"{o}f intensional type theory, which is sound and complete for the 1-truncated version of the theory. The model formally combines the syntactic model with a notion of realizability; it also…
We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin. One level is given by an intensional type theory, called Minimal type theory. This theory extends the set-theoretic version…
Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…
We provide a simple proof of the existence of internal Homs in the localization of the category of dg categories with respect to all quasi-equivalences and of some of their main properties such as the so-called derived Morita theory. This…
Hausdorff Morita equivalence is an equivalence relation on singular foliations, which induces a bijection between their leaves. Our main statement is that linearizability along a leaf is invariant under Hausdorff Morita equivalence. The…
Hrushovski's suggestion, given in ["Groupoids, imaginaries and internal covers," Turkish Journal of Mathematics , 2012], to capture the structure of the 1-analysable covers of a theory T using simplicial groupoids definable in T is realized…
We explore recursive programming with extensible data types. Row types make the structure of data types first class, and can express a variety of type system features including record subtyping and combination of case branches. Our goal is…
In Feferman's work, explicit mathematics and theories of generalized inductive definitions play a central role. One objective of this article is to describe the connections with Martin-Lof type theory and constructive Zermelo-Fraenkel set…
This paper introduces an expressive class of quotient-inductive types, called QW-types. We show that in dependent type theory with uniqueness of identity proofs, even the infinitary case of QW-types can be encoded using the combination of…
This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an…
A paraconsistent type theory (an extension of a fragment of intuitionistic type theory by adding opposite types) is here extended by adding co-function types. It is shown that, in the extended paraconsistent type system, the opposite type…
Cubical type theory provides a constructive justification to certain aspects of homotopy type theory such as Voevodsky's univalence axiom. This makes many extensionality principles, like function and propositional extensionality, directly…
In this paper we split every basic propositional connective into two versions, one is called extensional and the other one intensional. The extensional connectives are semantically characterized by standard truth conditions that are…