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Orthogonality is a notion based on the duality between programs and their environments used to determine when they can be safely combined. For instance, it is a powerful tool to establish termination properties in classical formal systems.…

Logic in Computer Science · Computer Science 2024-02-14 Marcelo Fiore , Zeinab Galal , Farzad Jafarrahmani

Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the…

Logic · Mathematics 2023-06-22 Nick Bezhanishvili , Jim de Groot , Yde Venema

We address the task of deriving fixpoint equations from modal logics characterizing behavioural equivalences and metrics (summarized under the term conformances). We rely on earlier work that obtains Hennessy-Milner theorems as corollaries…

Logic in Computer Science · Computer Science 2024-02-01 Harsh Beohar , Sebastian Gurke , Barbara König , Karla Messing , Jonas Forster , Lutz Schröder , Paul Wild

Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are…

Logic in Computer Science · Computer Science 2017-03-20 Marcello M. Bonsangue , Stefan Milius , Alexandra Silva

We introduce and investigate the notion of uniform Lyndon interpolation property (ULIP) which is a strengthening of both uniform interpolation property and Lyndon interpolation property. We prove several propositional modal logics including…

Logic · Mathematics 2020-01-14 Taishi Kurahashi

Our objective is to extend the standard results of preservation and reflection of properties by bisimulations to the coalgebraic setting, as well as to study under what conditions these results hold for simulations. The notion of…

Logic in Computer Science · Computer Science 2024-02-05 Ignacio Fábregas , Miguel Palomino , David de Frutos-Escrig

We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…

Logic · Mathematics 2016-09-06 Alessandra Carbone

There is a wide range of modal logics whose semantics goes beyond relational structures, and instead involves, e.g., probabilities, multi-player games, weights, or neighbourhood structures. Coalgebraic logic serves as a unifying semantic…

Logic in Computer Science · Computer Science 2023-06-16 Oliver Görlitz , Daniel Hausmann , Merlin Humml , Dirk Pattinson , Simon Prucker , Lutz Schröder

Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as…

Logic in Computer Science · Computer Science 2019-08-09 Simone Barlocco , Clemens Kupke , Jurriaan Rot

We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual…

Symbolic Computation · Computer Science 2012-03-19 C. Baier , N. Bertrand , Ph. Schnoebelen

To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015 Recent advances in knowledge compilation introduced techniques to compile \emph{positive} logic programs into propositional logic, essentially exploiting…

Logic in Computer Science · Computer Science 2020-02-19 Bart Bogaerts , Guy Van den Broeck

We focus on the persistence principle over weak interpretability logic. Our object of study is the logic obtained by adding the persistence principle to weak interpretability logic from several perspectives. Firstly, we prove that this…

Logic · Mathematics 2023-10-03 Sohei Iwata , Taishi Kurahashi , Yuya Okawa

A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…

Rings and Algebras · Mathematics 2009-10-30 James Worthington

Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown,…

Logic · Mathematics 2019-04-15 S. J. v. Gool , G. Metcalfe , C. Tsinakis

Uniform interpolation is a strong form of interpolation providing an interpretation of propositional quantifiers within a propositional logic. Pitts' seminal work establishes this property for intuitionistic propositional logic relying on a…

Logic in Computer Science · Computer Science 2026-05-28 Iris van der Giessen , Ian Shillito

The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this…

Logic in Computer Science · Computer Science 2016-11-23 Corina Cirstea , Clemens Kupke , Dirk Pattinson

This paper contributes to a theory of the behaviour of "finite-state" systems that is generic in the system type. We propose that such systems are modelled as coalgebras with a finitely generated carrier for an endofunctor on a locally…

Logic in Computer Science · Computer Science 2019-09-09 Stefan Milius , Dirk Pattinson , Thorsten Wißmann

We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…

Logic in Computer Science · Computer Science 2023-06-22 Michael Benedikt , Pierre Bourhis , Michael Vanden Boom

We present a proof-theoretical study of the interpretability logic IL, providing a wellfounded and a non-wellfounded sequent calculus for IL. The non-wellfounded calculus is used to establish a cut elimination argument for both calculi. In…

Logic · Mathematics 2025-11-04 Sebastijan Horvat , Borja Sierra Miranda , Thomas Studer

A variety V is said to be coherent if any finitely generated subalgebra of a finitely presented member of V is finitely presented. It is shown here that V is coherent if and only if it satisfies a restricted form of uniform deductive…

Logic · Mathematics 2018-03-28 Tomasz Kowalski , George Metcalfe