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We present a sequent-style proof system for provability logic GL that admits so-called circular proofs. For these proofs, the graph underlying a proof is not a finite tree but is allowed to contain cycles. As an application, we establish…
Extensibility is beyond the paradigm of classical soft glassy materials, and more broadly, yield-stress fluids. Recently, model yield-stress fluids with significant extensibility have been designed by adding polymeric phases to classically…
Subset models provide a new semantics for justifcation logic. The main idea of subset models is that evidence terms are interpreted as sets of possible worlds. A term then justifies a formula if that formula is true in each world of the…
We introduce $\mathcal{DLR}^+$, an extension of the n-ary propositionally closed description logic $\mathcal{DLR}$ to deal with attribute-labelled tuples (generalising the positional notation), projections of relations, and global and local…
The differential $\lambda$-calculus studies how the quantitative aspects of programs correspond to differentiation and to Taylor expansion inside models of linear logic. Recent work has generalized the axioms of Taylor expansion so they…
When performing complex multi-step reasoning tasks, the ability of Large Language Models (LLMs) to derive structured intermediate proof steps is important for ensuring that the models truly perform the desired reasoning and for improving…
Max-Plus Linear (MPL) systems are an algebraic formalism with practical applications in transportation networks, manufacturing and biological systems. In this paper, we investigate the problem of automatically analyzing the properties of…
In this paper, we investigate the proof complexity of a wide range of substructural systems. For any proof system $\mathbf{P}$ at least as strong as Full Lambek calculus, $\mathbf{FL}$, and polynomially simulated by the extended Frege…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
We advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The…
The provability logic of a theory T is the set of modal formulas, which under any arithmetical realization are provable in T . We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$.…
Filler-induced strengthening is ubiquitous in materials science and is particularly well-established in polymeric nanocomposites. Despite having similar constituents, colloidal gels with solid filling exhibit distinct rheology, which is of…
Metric Temporal Logic (MTL) is a prominent specification formalism for real-time systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also…
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also…
As large language models (LLMs) become increasingly powerful, traditional evaluation metrics tend to saturate, making it challenging to distinguish between models. We propose a general method to transform existing LLM evaluations into a…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Large Language Models (LLMs) have demonstrated impressive capabilities in complex reasoning tasks, yet they still struggle to reliably verify the correctness of their own outputs. Existing solutions to this verification challenge often…
Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…