Related papers: Learning Definite Horn Formulas from Closure Queri…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
This paper is a contribution to the study of the universal Horn fragment of predicate fuzzy logics, focusing on the proof of the existence of free models of theories of Horn clauses over Rational Pavelka predicate logic. We define the…
We propose a version of the Hodge conjecture in Bott-Chern cohomology and using results from characterizing real holomorphic chains by real rectifiable currents to provide a proof for this question. We define a Bott-Chern differential…
In a type-theoretic fibration category in the sense of Shulman (representing a dependent type theory with at least 1, Sigma, Pi, and identity types), we define the type of constant functions from A to B. This involves an infinite tower of…
It is known that the verification of imperative, functional, and logic programs can be reduced to the satisfiability of constrained Horn clauses (CHCs), and this satisfiability check can be performed by using CHC solvers, such as Eldarica…
When working in a proof assistant, automation is key to discharging routine proof goals such as equations between algebraic expressions. Homotopy type theory allows the user to reason about higher structures, such as topological spaces,…
We present a novel definition of an algorithm and its corresponding algorithm language called CoLweb. The merit of CoLweb [1] is that it makes algorithm design so versatile. That is, it forces us to a high-level, proof-carrying,…
In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…
Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be…
Constraint Handling Rules (CHR) are a committed-choice declarative language which has been designed for writing constraint solvers. A CHR program consists of multi-headed guarded rules which allow one to rewrite constraints into simpler…
An algebraic theory, sometimes called an equational theory, is a theory defined by finitary operations and equations, such as the theories of groups and of rings. It is well known that algebraic theories are equivalent to finitary monads on…
Given a universal Horn formula of Kleene algebra with hypotheses of the form r = 0, it is already known that we can efficiently construct an equation which is valid if and only if the Horn formula is valid. This is an example of…
Autonomous systems that operate in a shared environment with people need to be able to follow the rules of the society they occupy. While laws are unique for one society, different people and institutions may use different rules to guide…
Kuhn-Tucker points play a fundamental role in the analysis and the numerical solution of monotone inclusion problems, providing in particular both primal and dual solutions. We propose a class of strongly convergent algorithms for…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
The standard techniques for online learning of combinatorial objects perform multiplicative updates followed by projections into the convex hull of all the objects. However, this methodology can be expensive if the convex hull contains many…
The Horn inequalities characterise the possible spectra of triples of $n$-by-$n$ Hermitian matrices $A+B=C$. We study integral inequalities that arise as limits of Horn inequalities as $n \to \infty$. These inequalities are parametrised by…
We investigate the concept of definable, or inner, automorphism in the logical setting of partial Horn theories. The central technical result extends a syntactical characterization of the group of such automorphisms (called the covariant…
We develop a framework that systematically casts the solvability and uniqueness conditions of linearized geometric boundary-value problems into cohomological terms. The theory is designed to be applicable without assumptions on the…
Computing homology and cohomology is at the heart of many recent works and a key issue for topological data analysis. Among homological objects, homology generators are useful to locate or understand holes (especially for geometric…