Starting from the notions of q-entailment and p-entailment, a two-dimensional notion of entailment is developed with respect to certain generalized q-matrices referred to as B-matrices. After showing that every purely monotonic singleconclusion consequence relation is characterized by a class of B-matrices with respect to q-entailment as well as with respect to p-entailment, it is observed that, as a result, every such consequence relation has an inferentially four-valued characterization. Next, the canonical form of B-entailment, a two-dimensional multiple-conclusion notion of entailment based on B-matrices, is introduced, providing a uniform framework for studying several different notions of entailment based on designation, antidesignation, and their complements. Moreover, the two-dimensional concept of a B-consequence relation is defined, and an abstract characterization of such relations by classes of B-matrices is obtained. Finally, a contribution to the study of inferential many-valuedness is made by generalizing Suszko's Thesis and the corresponding reduction to show that any B-consequence relation is, in general, inferentially four-valued.An Inferentially Many-Valued Two-Dimensional Notion of Entailment 235 of a p-matrix [7,8]. A q-matrix (quasi matrix) is a structure A, D + , D − , where A is an algebra similar to a propositional language L, and where D + and D − are subsets of A, and D + ∩ D − = ∅. Usually, D + is referred to as the set of designated values and D − as the set of antidesignated values. A p-matrix (plausibility matrix) is a structure A, D + , D * , where A is an algebra similar to a propositional language L and D + ⊆ D * ⊆ A. The set D * is usually referred to as the set of plausible, non-antidesignated values.We adopt a compact notation that avoids superscripts and the barnotation for set-theoretic complementation, introducing the symbols Y, Y , N, and N to denote, respectively, the sets of designated, non-designated (V \ Y), antidesignated, and non-antidesignated (V \N) values. With a cognitive twist, they might be taken as representing acceptance, non-acceptance, rejection and non-rejection. 1

The standard notion of formal theory, in Logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by allowing one to take both assertions and denials on a par. This novel notion of theory is based on a bilateralist approach to consequence operators, which we hereby introduce, and whose main properties we investigate in the present paper.

Informação sobre o artigo CDD: Recebido: . . ; Revisado: . . ; Aceito: . . DOI: http://dx.doi.org/ . / -. .V N .CB Palavras-chaves / Keywords Lógica de Dunn-Belnap / Dunn-Belnap's Logic Relação de consequência / Consequence relation Semânticas multivaloradas / Many-valued semantics RESUMOO presente artigo apresenta uma semântica baseada nas atitudes cognitivas de aceitação e rejeição por uma sociedade de agentes para lógicas inspiradas no First Degree Entailment (E) de Dunn e Belnap. Diferente das situações epistêmicas originalmente usadas em E, as atitudes cognitivas não coincidem com valores-de-verdade e parecem mais adequadas para as lógicas que pretendem considerar o conteúdo informacional de proposições "ditas verdadeiras" tanto quanto as proposições "ditas falsas" como determinantes da noção de validade das inferências. Após analisar algumas lógicas associadas à semântica proposta, introduzimos a lógica E B cuja relação de consequência semântica subjacente -o B-entailment-é capaz de expressar diversos tipos de raciocínio em relação às atitudes cognitivas de aceitação e rejeição. Apresentamos também um cálculo de sequentes correto e completo para E B . ABSTRACTIn the present work I introduce a semantics based on the cognitive attitudes of acceptation and rejection entertained by a given society of agents for logics inspired on Dunn and Belnap's 'First Degree Entailment' (E). Distinctly from the original epistemic situation of E, the cognitive attitudes do not coincide with truth-values and it seems more suitable for logics that intend to consider the informational content of propositions "said to be true" as well as propositions "said to be false" as determinants of the notion of logical validity. After analyzing some logics associated with the proposed semantics, we introduce the logic E B , whose underlying semantic entailment relation -the B-entailment-is able to express several kinds of reasoning towards the cognitive attitudes of acceptance and rejection. A correct and complete sequent calculus for E B is also presented. -Rev. Int. Fil., Campinas, v. , n. , pp. -, abr.-jun. . Manuscrito

Le constat du rejet total ou partiel de la théorie de l’évolution au nom de motifs religieux par des élèves dans différents pays amène à s’interroger – plus globalement – sur les facteurs influençant l’adoption ou non-adoption d’une conception sécularisée de la science. Cette recherche vise à examiner, à partir d’un questionnaire à réponses fermées, l’influence de deux facteurs : les convictions personnelles des élèves en matière de religion et la filière d’études (scientifique ou non). L’enquête a été réalisée dans sept pays présentant des caractéristiques différenciées en matière de sécularisation : la Belgique, l’Espagne, l’Italie, la Côte d’Ivoire, la République démocratique du Congo, le Maroc et la Turquie.