Related papers: Algorithmic correspondence and canonicity for non-…
We study the correspondence theory of intuitionistic modal logic in modal Fairtlough-Mendler semantics (modal FM semantics) \cite{FaMe97}, which is the intuitionistic modal version of possibility semantics \cite{Ho16}. We identify the…
Current large language models reason in isolation. Although it is common to sample multiple reasoning paths in parallel, these trajectories do not interact, and often fail in the same redundant ways. We introduce LACE, a framework that…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
We introduce a new fragment of Linear temporal logic (LTL) called LIO and a new class of Buechi automata (BA) called Almost linear Buechi automata (ALBA). We provide effective translations between LIO and ALBA showing that the two…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
We survey some of the mechanisms used to prove that naturally defined sequences in combinatorics are log-concave. Among these mechanisms are Alexandrov's inequality for mixed discriminants, the Alexandrov Fenchel inequality for mixed…
We study how the existence in an algebraic lattice $L$ of a chain of a given type is reflected in the join-semilattice $K(L)$ of its compact elements. We show that for every chain $\alpha$ of size $\kappa$, there is a set $\B$ of at most…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
This paper pursues an investigation on groups equipped with an $L$-ordered relation, where $L$ is a fixed complete complete Heyting algebra. First, by the concept of join and meet on an $L$-ordered set, the notion of an $L$-lattice is…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
We prove a uniform version of the Goldblatt-Thomason theorem for logics algebraically captured by normal lattice expansions (normal LE-logics).
We present a functorial construction which, starting from a congruence $\alpha$ of finite index in an algebra A, yields a new algebra C with the following properties: the congruence lattice of C is isomorphic to the interval of congruences…
This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…
We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono's algebraic approach to substructural logics. We propose generalized BI algebras (GBI-algebras) as a common framework…
Assuming a large cardinal hypothesis, Laver gave a representation of the monogenerated free left distributive algebra (LDA) using elementary embeddings and used this representation to prove many algebraic results. Some of these results were…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
We take a long magical tour in algebraic logic, starting from classical results on neat embeddings due to Henkin, Monk and Tarski, all the way to recent results in algebraic logic using so--called rainbow constructions invented by Hirsch…
The calculus of classes and closure operations has proved to be a useful tool in group theory and has led to a deep theory in the study of finite soluble groups. More recently, parallel theories have started to be developed in various…