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Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
There are representations of the type-A Hecke algebra on spaces of polynomials in anti-commuting variables. Luque and the author [S\'em. Lothar. Combin. 66 (2012), Art. B66b, 68 pages, arXiv:1106.0875] constructed nonsymmetric Macdonald…
This paper considers KLM-style preferential non-monotonic reasoning in the setting of propositional team semantics. We show that team-based propositional logics naturally give rise to cumulative non-monotonic entailment relations. Motivated…
This paper examines the asymptotic convergence properties of Lipschitz interpolation methods within the context of bounded stochastic noise. In the first part of the paper, we establish probabilistic consistency guarantees of the classical…
An algorithm for generating interpolants for formulas which are conjunctions of quadratic polynomial inequalities (both strict and nonstrict) is proposed. The algorithm is based on a key observation that quadratic polynomial inequalities…
First, we prove the Kac-Wakimoto conjecture on modular invariance of characters of exceptional affine W-algebras. In fact more generally we prove modular invariance of characters of all lisse W-algebras obtained through Hamiltonian…
The monograph contains the detailed exposition of the results obtained by the author during the last several years. In particular it contains an improvement of the well known Calderon - Ryff interpolation theorem and description of…
Feasible interpolation is a general technique for proving proof complexity lower bounds. The monotone version of the technique converts, in its basic variant, lower bounds for monotone Boolean circuits separating two NP-sets to proof…
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…
We combine the concepts of modal logics and many-valued logics in a general and comprehensive way. Namely, given any finite linearly ordered set of truth values and any set of propositional connectives defined by truth tables, we define the…
Affine continuous logic is extended to affine integration logic. Affine compactness theorem is proved by both the ultramean construction and Henkin's method. Also, a proof system and a completeness theorem are given. An appropriate variant…
There is a recent interest for the verification of monadic programs using proof assistants. This line of research raises the question of the integration of monad transformers, a standard technique to combine monads. In this paper, we extend…
The aim of this paper is to show that even if the natural algebraic semantic for modal (normal) logic is modal algebra, the more general class of subordination algebras (roughly speaking, the non symmetric contact algebras) is adequate too…
Abstract. Matching logic cannot handle concurrency. We introduce concurrent matching logic (CML) to reason about fault-free partial correctness of shared-memory concurrent programs. We also present a soundness proof for concurrent matching…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…
We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to the case of symmetric implication calculus $\mathsf{S^2IC}$,…
Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…
Model merging, typically on Instruct and Thinking models, has shown remarkable performance for efficient reasoning. In this paper, we systematically revisit the simplest merging method that interpolates two weights directly. Particularly,…
We show that a proof in multiplicative linear logic can be represented as a decorated surface, such that two proofs are logically equivalent just when their surfaces are geometrically equivalent. This is an extended abstract for…