Related papers: Kleene Algebra Modulo Theories
Universal multimodal embedding (UME) maps heterogeneous inputs into a shared retrieval space with a single model. Recent approaches improve UME by generating explicit chain-of-thought (CoT) rationales before extracting embeddings, enabling…
We consider algebras of languages over the signature of reversible Kleene lattices, that is the regular operations (empty and unit languages, union, concatenation and Kleene star) together with intersection and mirror image. We provide a…
We generalize Kracht's theory of internal describability from classical modal logic to the family of all logics canonically associated with varieties of normal lattice expansions (LE algebras). We work in the purely algebraic setting of…
Large language models (LLMs) exhibit in-context learning abilities which enable the same model to perform several tasks without any task-specific training. In contrast, traditional adaptation approaches, such as fine-tuning, modify the…
Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but…
Large language models have demonstrated impressive performance across many domains of mathematics and physics. One natural question is whether such models can support research in highly abstract theoretical fields such as quantum field…
We investigate the equational theory for Kleene algebra terms with variable complements and constant complements -- (language) complement where it applies only to variables or constants -- w.r.t. languages. While the equational theory…
We aim at a holistic perspective on program logics, including Hoare and incorrectness logics. To this end, we study different classes of properties arising from the generalization of the aforementioned logics. We compare our results with…
Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. While existing gradual type soundness theorems for these languages aim to show that…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…
We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution…
This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules. We adopt the constructive point of view, with which all existence theorems have an explicit algorithmic…
We study modal team logic MTL, the team-semantical extension of modal logic ML closed under Boolean negation. Its fragments, such as modal dependence, independence, and inclusion logic, are well-understood. However, due to the unrestricted…
Energy problems are important in the formal analysis of embedded or autonomous systems. Using recent results on star-continuous Kleene omega-algebras, we show here that energy problems can be solved by algebraic manipulations on the…
Superposed coherent states are central to quantum technologies, yet their reliable identification remains a challenge, especially in noisy or resource-constrained settings. We introduce a novel, directly measurable criterion for detecting…
The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see…
Formal theories of arithmetic have traditionally been based on either classical or intuitionistic logic, leading to the development of Peano and Heyting arithmetic, respectively. We propose to use $\mu$MALL as a formal theory of arithmetic…
We present MatchKAT, an algebraic language for modeling match-action packet processing in network switches. Although the match-action paradigm has remained a popular low-level programming model for specifying packet forwarding behavior,…
Automata operating on pairs of words were introduced as an alternative way of capturing acceptance of regular $\omega$-languages. Families of DFAs and lasso automata operating on such pairs followed, giving rise to minimisation algorithms,…