Related papers: Pure Type Systems without Explicit Contexts
The study of homotopy theoretic phenomena in the language of type theory is sometimes loosely called `synthetic homotopy theory'. Homotopy theory in type theory is only one of the many aspects of homotopy type theory, which also includes…
We present the definition of the logical framework TF, the Type Framework. TF is a lambda-free logical framework; it does not include lambda-abstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and…
Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…
In this paper, based on results of exact learning and test theory, we study arbitrary infinite binary information systems each of which consists of an infinite set of elements and an infinite set of two-valued functions (attributes) defined…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
Graphs are a generalized concept that encompasses more complex data structures than trees, such as difference lists, doubly-linked lists, skip lists, and leaf-linked trees. Normally, these structures are handled with destructive assignments…
We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations. The type theory imposes an…
We propose a method of classifying the operation of a system into finitely many modes. Each mode has its own objectives for the system's behaviour and its own mathematical models and algorithms designed to accomplish its objectives. A…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
In this paper I survey the sources of inspiration for my own and co-authored work in trying to develop a general theory of graph polynomials. I concentrate on meta-theorems, i.e., theorem which depend only on the form infinite classes of…
We define a simple dependent type theory and prove that its well-formed types correspond exactly to finite inverse categories.
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…
We present a new strictification method for type-theoretic structures that are only weakly stable under substitution. Given weakly stable structures over some model of type theory, we construct equivalent strictly stable structures by…
We give a procedure that can be used to automatically satisfy invariants of a certain shape. These invariants may be written with the operations intersection, composition and converse over binary relations, and equality over these…
Curry-style system F, ie. system F with no explicit types in terms, can be seen as a core presentation of polymorphism from the point of view of programming languages. This paper gives a characterisation of type isomorphisms for this…
We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type…
We use type-theoretic techniques to present an algebraic theory of $\infty$-categories with strict units. Starting with a known type-theoretic presentation of fully weak $\infty$-categories, in which terms denote valid operations, we extend…
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…
The role of types in categorical models of meaning is investigated. A general scheme for how typed models of meaning may be used to compare sentences, regardless of their grammatical structure is described, and a toy example is used as an…