Related papers: An Abstract Approach to Consequence Relations

A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing…

An abstract linking result for Cerami sequences is proved without the Cerami condition. It is applied directly in order to prove the existence of critical points for a class of indefinite problems in infinite dimensional Hilbert Spaces. The…

We propose a generalization of Categorial Grammar in which lexical categories are defined by means of recursive constraints. In particular, the introduction of relational constraints allows one to capture the effects of (recursive) lexical…

Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose…

The study of causal relationships between emotions and causes in texts has recently received much attention. Most works focus on extracting causally related clauses from documents. However, none of these works has considered that the causal…

MSO transductions are binary relations between structures which are defined using monadic second-order logic. MSO transductions form a category, since they are closed under composition. We show that many notions from language theory, such…

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of…

The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…

We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a…

This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…

An elementary rheory of concatenation is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, the quantifier-free part of Kirby's finitary set theory, and Adjunctive Set Theory,…

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 generalize three results of M. Aguiar, which are valid for Loday's dendriform algebras, to arbitrary dendriform algebras, i.e., dendriform algebras associated to algebras satisfying any given set of relations. We define these dendriform…

In this thesis, a detailed study shows that closed itemsets and minimal generators play a key role for concisely representing both frequent itemsets and association rules. These itemsets structure the search space into equivalence classes…

In order to be able to use methods of Universal Algebra for investigating posets, we assign to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset a certain algebra…

We establish a theory of complexes of relative correspondences. The theory generalizes the known theory of complexes of correspondences of smooth projective varieties. It will be applied in the sequel of this paper to the construction of…

We propose here a multidimensional generalisation of the notion of link introduced in our previous papers and we discuss some consequences for simplicial measures and sums of function algebras.

The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…

This paper presents a novel concept of a Polyatomic Logic and initiates its systematic study. This approach, inspired by Inquisitive semantics, is obtained by taking a variant of a given logic, obtained by looking at the fragment covered by…

A central challenge for cognitive science is to explain how abstract concepts are acquired from limited experience. This has often been framed in terms of a dichotomy between connectionist and symbolic cognitive models. Here, we highlight a…