Related papers: Sequent Calculi for Data-Aware Modal Logics
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality $!_r$ captures how many times a…
We present a modification of the superposition calculus that is meant to generate explanations why a set of clauses is satisfiable. This process is related to abductive reasoning, and the explanations generated are clauses constructed over…
Szlach\'anyi's skew monoidal categories are a well-motivated variation of monoidal categories in which the unitors and associator are not required to be natural isomorphisms, but merely natural transformations in a particular direction. We…
Building on our previous work on hybrid polyadic modal logic we identify modal logic equivalents for Matching Logic, a logic for program specification and verification. This provides a rigorous way to transfer results between the two…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
This paper employs the linear nested sequent framework to design a new cut-free calculus LNIF for intuitionistic fuzzy logic--the first-order G\"odel logic characterized by linear relational frames with constant domains. Linear nested…
The finite cell method is a highly flexible discretization technique for numerical analysis on domains with complex geometries. By using a non-boundary conforming computational domain that can be easily meshed, automatized computations on a…
We define base-extension semantics (Bes) using atomic systems based on sequent calculus rather than natural deduction. While traditional Bes aligns naturally with intuitionistic logic due to its constructive foundations, we show that…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough…
This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
This technical report provides some lightweight introduction motivating the definition of an alignment of log traces against Data-Aware Declare Models potentially containing correlation conditions. This technical report is only providing…
We present a proof system for the provability logic GLP in the formalism of nested sequents and prove the cut elimination theorem for it. As an application, we obtain the reduction of GLP to its important fragment called J syntactically.
We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen's classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less…
Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…