Related papers: Uniform Interpolation for Coalgebraic Fixpoint Log…

Automata admitting at most one accepting run per structure, known as unambiguous automata, find applications in verification of reactive systems as they extend the class of deterministic automata whilst maintaining some of their desirable…

We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.

A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform…

This note points out a lemma on closures of monotonic increasing functions and shows how it is applicable to decomposition and modularity for semantics defined as the least fixedpoint of some monotonic function. In particular it applies to…

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…

In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…

This paper gives two new categorical characterisations of lenses: one as a coalgebra of the store comonad, and the other as a monoidal natural transformation on a category of a certain class of coalgebras. The store comonad of the first…

We study different representation theorems for various reducts of Heyting polyadic algebras. Superamalgamation is proved for several (natural reducts) and our results are compared to the finitizability problem in classical algebraic logic…

We consider interpolation from the viewpoint of fully automated theorem proving in first-order logic as a general core technique for mechanized knowledge processing. For Craig interpolation, our focus is on the two-stage approach, where…

We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…

The paper aims to develop a framework for coalgebraic fuzzy geometric logic by adding modalities to the language of fuzzy geometric logic. Using the methods of coalgebra, the modal operators are introduced in the language of fuzzy geometric…

This paper presents experiments on common knowledge logic, conducted with the help of the proof assistant Coq. The main feature of common knowledge logic is the eponymous modality that says that a group of agents shares a knowledge about a…

We solve fundamental problems in Oka theory by establishing an implicit function theorem for sprays. As the first application of our implicit function theorem, we obtain an elementary proof of the fact that approximation yields…

Motivated by questions like: which spatial structures may be characterized by means of modal logic, what is the logic of space, how to encode in modal logic different geometric relations, topological logic provides a framework for studying…

We consider interpolation learning in high-dimensional linear regression with Gaussian data, and prove a generic uniform convergence guarantee on the generalization error of interpolators in an arbitrary hypothesis class in terms of the…

Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…

Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…

We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in…

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…

The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…