Related papers: Subexponentials in non-commutative linear logic

We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill's calculi, and focus on their fragments…

We investigate the phenomenon of non-recursive trade-offs between descriptional systems in an abstract fashion. We aim at categorizing non-recursive trade-offs by bounds on their growth rate, and show how to deduce such bounds in general.…

Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…

Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of…

This paper proposes a basic proof theoretic framework for major modal logics: {\sf S5} and some of its subsystems. The framework is based on a version of hypersequent calculus, and the basic modal systems we handle here are the system {\sf…

Infinitary and cyclic proof systems are proof systems for logical formulas with fixed-point operators or inductive definitions. A cyclic proof system is a restriction of the corresponding infinitary proof system. Hence, these proof systems…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…

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.…

Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in English natural language. While the progress is promising, it is currently unclear if these models…

This paper provides an NP procedure that decides whether a linear-exponential system of constraints has an integer solution. Linear-exponential systems extend standard integer linear programs with exponential terms $2^x$ and remainder terms…

We present a syntactic cut-elimination procedure for the alternation-free fragment of the modal mu-calculus. Cut reduction is carried out within a cyclic proof system, where proofs are finitely branching but may be non-wellfounded. The…

We extend the framework of abstract algebraic logic to weak logics, namely logical systems which are not necessarily closed under uniform substitution. We interpret weak logics by algebras expanded with an additional predicate and we…

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…

As larger deep learning models are hard to interpret, there has been a recent focus on generating explanations of these black-box models. In contrast, we may have apriori explanations of how models should behave. In this paper, we formalize…

Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies…

Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…

Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…

Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled…

The purpose of this article is to describe and characterize the limit distributions of translates of a bounded open "piece of orbit" of a reductive subgroup on a space of S-arithmetic lattices. This is accomplished under a mild assumption…