Related papers: Functorial Semantics for Partial Theories

Based on Gandy's principles for models of computation we give category-theoretic axioms describing locally deterministic updates to finite objects. Rather than fixing a particular category of states, we describe what properties such a…

We extend the logical categories framework to first order modal logic. In our modal categories, modal operators are applied directly to subobjects and interact with the background factorization system. We prove a Joyal-style representation…

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

A theory of a derivator version of six-functor-formalisms is developed, using an extension of the notion of fibered multiderivator due to the author. Using the language of (op)fibrations of 2-multicategories this has (like a usual fibered…

We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…

This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…

We present a doctrinal approach to category theory, obtained by abstracting from the indexed inclusions (via discrete fibrations and opfibrations) of the left and of the right actions of X in Cat in categories over X. Namely, a "weak…

We first recall some basic notions on minimalist grammars and on categorial grammars. Next we shortly introduce partially commutative linear logic, and our representation of minimalist grammars within this categorial system, the so-called…

The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…

In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…

We introduce a notion of (co)presheaf on a lax double functor $X$, which we generally call an instance. In the terminology of double-categorical logic, a lax double functor valued in sets, possibly preserving finite products, is called a…

A perspective of statistical language models which emphasizes their collocational aspect is advocated. It is suggested that strings be generalized in terms of classes of relationships instead of classes of objects. The single most important…

Temporal logic provided an appealing approach to specifying properties of operating systems and other "reactive" software by allowing propositions to be qualified by "when" they must be true. This paper shows how to get the same effect,…

We investigate the extent to which Linear Temporal Logic (LTL) formulas can be uniquely characterized by a finite set of labeled examples. We consider different types of examples, ranging from finite words to transfinite words, as well as…

Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…

A wide range of intuitionistic type theories may be presented as equational theories within a logical framework. This method was formulated by Per Martin-L\"{o}f in the mid-1980's and further developed by Uemura, who used it to prove an…

The notions of formal contexts and concept lattices, although introduced by Wille only ten years ago, already have proven to be of great utility in various applications such as data analysis and knowledge representation. In this paper we…

Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…

We propose an abstract definition of convex spaces as sets where one can take convex combinations in a consistent way. A priori, a convex space is an algebra over a finitary version of the Giry monad. We identify the corresponding Lawvere…

In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…