Related papers: A Note on One Less Known Class of Generated Residu…

When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce the connective implication to be everywhere defined and satisfying (left) adjointness with the connective…

In the area of inductive learning, generalization is a main operation, and the usual definition of induction is based on logical implication. Recently there has been a rising interest in clausal representation of knowledge in machine…

We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…

Since orthomodular posets serve as an algebraic axiomatization of the logic of quantum mechanics, it is a natural question how the connective of implication can be defined in this logic. It should be introduced in such a way that it is…

The clausal logical consequences of a formula are called its implicates. The generation of these implicates has several applications, such as the identification of missing hypotheses in a logical specification. We present a procedure that…

We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is…

Apart from a brief look at applications (Relational Databases, Formal Concept Analysis, data mining) this article is devoted to the mathematical t h e o r y of implications (=pure Horn formulas). It is mainly a survey of results obtained in…

We introduce a~\textit{Choquet-Sugeno-like operator} generalizing many operators for bounded functions and monotone measures from the literature, e.g., Sugeno-like operator, Lov\'{a}sz and Owen measure extensions, $\rF$-decomposition…

Let T be Goedel's system of primitive recursive functionals of finite type in the lambda formulation. We define by constructive means using recursion on nested multisets a multivalued function I from the set of terms of T into the set of…

In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a…

This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material…

With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…

In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…

Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…

A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such…

Given two sets of elements (such as cell types and drug compounds), researchers typically only have access to a limited subset of their interactions. The task of causal imputation involves using this subset to predict unobserved…

Following the work of Beilinson, Bernstein and Deligne, we study restriction and induction of t-structures in triangulated categories with respect to recollements. For derived categories of piecewise hereditary algebras we give a necessary…

Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate…

Causal inference uses observations to infer the causal structure of the data generating system. We study a class of functional models that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual…

In a paper published in 2012, the second author extended the well-known fact that Boolean algebras can be defined using only implication and a constant, to De Morgan algebras-this result led him to introduce, and investigate (in the same…