Related papers: Unification of Deterministic Higher-Order Patterns…
Bezem, Coquand, and Huber have recently given a constructively valid model of higher type theory in a category of nominal cubical sets satisfying a novel condition, called the uniform Kan condition (UKC), which generalizes the standard…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies.…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Pulman has shown that Higher--Order Unification (HOU) can be used to model the interpretation of focus. In this paper, we extend the unification--based approach to cases which are often seen as a test--bed for focus theory: utterances with…
In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem originally established by…
An uncomplicated and easily handling prescription that converts the task of checking the unitarity of massive, topologically massive, models into a straightforward algebraic exercise, is developed. The algorithm is used to test the…
There exist two known canonical types of ultrafilter extensions of first-order models; one comes from modal logic and universal algebra, another one from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as…
The unification type of an equational theory is defined using a preorder on substitutions, called the instantiation preorder, whose scope is either restricted to the variables occurring in the unification problem, or unrestricted such that…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…
Gauge-Yukawa Unification (GYU) yields a functional relation among the gauge and Yukawa couplings, and it may follow from the usual Grand Unification if it is supplemented with some additional principles. Postulating the principles of…
We introduce a novel framework, termed $\lambda$DD, that revisits Binary Decision Diagrams from a purely functional point of view. The framework allows to classify the already existing variants, including the most recent ones like Chain-DD…
Equational unification of two terms consists of finding a substitution that, when applied to both terms, makes them equal modulo some equational properties. Equational unification is of special relevance to automated deduction, theorem…
We study the computational power that oblivious robots operating in the plane have under sequential schedulers. We show that this power is much stronger than the obvious capacity these schedulers offer of breaking symmetry, and thus to…
The notion of computability closure has been introduced for proving the termination of higher-order rewriting with first-order matching by Jean-Pierre Jouannaud and Mitsuhiro Okada in a 1997 draft which later served as a basis for the…
In this article, we explore federated customization of large models and highlight the key challenges it poses within the federated learning framework. We review several popular large model customization techniques, including full…
A natural gradual extension of the idea of Grand Unification is to attempt to relate the gauge and Yukawa couplings; Gauge-Yukawa Unification (GYU). However, within the framework of renormalizable field theories, there exists no realistic…
We review several problems of conventional Grand Unification and some new approaches. In particular, we discuss strongly coupled Grand Unified Theories. Standard Model may emerge as a low energy effective theory of composite particles in…
We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations'…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…