In our paper, monadic modal pseudocomplemented De Morgan algebras are considered following Halmos’ studies on monadic Boolean algebras. Hence, their topological representation theory is used successfully. Lattice congruences of an mmpM is characterized and the variety of mmpMs is proven semisimple via topological representation. Furthermore and among other things, the poset of principal congruences is investigated and proven to be a Boolean algebra; therefore, every principal congruence is a Boolean congruence. All these conclusions contrast sharply with known results for monadic (...) De Morgan algebras. Finally, we show that the above results for mmpM are verified for monadic tetravalent modal algebras. (shrink)

In this paper we investigate the class of MV-algebras equipped with two quantifiers which commute as a natural generalization of diagonal-free two-dimensional cylindric algebras. In the 40s, Tarski first introduced cylindric algebras in order to provide an algebraic apparatus for the study of classical predicate calculus. The diagonal–free two-dimensional cylindric algebras are special cylindric algebras. The treatment here of MV-algebras is done in terms of implication and negation. This allows us to simplify some results due to Di Nola and Grigolia (...) :125–139, 2004) related to the characterization of a quantifier in terms of some special sub-algebra associated to it. On the other hand, we present a topological duality for this class of algebras and we apply it to characterize the congruences of one algebra via certain closed sets. Finally, we study the subvariety of this class generated by a chain of length n + 1. We prove that the subvariety is semisimple and we characterize their simple algebras. Using a special functional algebra, we determine all the simple finite algebras of this subvariety. (shrink)

The IKt-algebras that we investigate in this paper were introduced in the paper An algebraic axiomatization of the Ewald’s intuitionistic tense logic by the first and third author. Now we characterize by topological methods the subdirectly irreducible IKt-algebras and particularly the simple IKt-algebras. Finally, we consider the particular cases of finite IKt-algebras and complete IKt-algebras.

The IKt-algebras were introduced in the paper An algebraic axiomatization of the Ewald’s intuitionistic tense logic by the first and third author. In this paper, our main interest is to investigate the principal and Boolean congruences on IKt-algebras. In order to do this we take into account a topological duality for these algebras obtained in Figallo et al. :673–701, 2017). Furthermore, we characterize Boolean and principal IKt-congruences and we show that Boolean IKt-congruence are principal IKt-congruences. Also, bearing in mind (...) the above results, we obtain that Boolean IKt-congruences are commutative, regular and uniform. Finally, we characterize the principal IKt-congruences in the case that the IKt-algebra is linear and complete whose prime filters are complete and also the case that it is linear and finite. This allowed us to establish that the intersection of two principal IKt-congruences on these algebras is a principal one and also to determine necessary and sufficient conditions so that a principal IKt-congruence is a Boolean one on theses algebras. (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

In this paper we present a category equivalent to that of tense Nelson algebras. The objects in this new category are pairs consisting of an IKt-algebra and a Boolean IKt-congruence and the morphisms are a special kind of IKt-homomorphisms. This categorical equivalence permits understanding tense Nelson algebras in terms of the better–known IKt-algebras.

In this paper, we continue the study of the Łukasiewicz residuation algebras of order $n$ with Moisil possibility operators initiated by Figallo. More precisely, among other things, a method to determine the number of elements of the $MC_n$-algebra with a finite set of free generators is described. Applying this method, we find again the results obtained by Iturrioz and Monteiro and by Figallo for the case of Tarski algebras and $I\varDelta _{3}$-algebras, respectively.

Modal pseudocomplemented De Morgan algebras were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 53, 1, pp. 65–79, and they constitute a proper subvariety of the variety of pseudocomplemented De Morgan algebras satisfying xΛ* = *))* studied by H. Sankappanavar in 1987. In this paper the study of these algebras is continued. More precisely, new characterizations of mpM-congruences are shown. In particular, one of them is (...) determined by taking into account an implication operation which is defined on these algebras as weak implication. In addition, the finite mpM-algebras were considered and a factorization theorem of them is given. Finally, the structure of the free finitely generated mpM-algebras is obtained and a formula to compute its cardinal number in terms of the number of the free generators is established. For characterization of the finitely-generated free De Morgan algebras, free Boole-De Morgan algebras and free De Morgan quasilattices see: [16, 17, 18]. (shrink)

In 2016, Béziau introduced the notion of genuine paraconsistent logic as logic that does not verify the principle of non-contradiction; as an important example, he presented the genuine paraconsist...

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...) the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)

In this paper, we continue with the study of tense operators on Nelson algebras (Figallo et al. in Studia Logica 109(2):285–312, 2021, Studia Logica 110(1):241–263, 2022). We define the variety of algebras, which we call tense Nelson D-algebras, as a natural extension of tense De Morgan algebras (Figallo and Pelaitay in Logic J IGPL 22(2):255–267, 2014). In particular, we give a discrete duality for these algebras. To do this, we will extend the representation theorems for Nelson algebras given (...) in Sendlewski (Studia Logica 43(3):257–280, 1984) to the tense case. (shrink)

In 2015, A.V. Figallo and G. Pelaitay introduced tense n×m-valued Łukasiewicz–Moisil algebras, as a common generalization of tense Boolean algebras and tense n-valued Łukasiewicz–Moisil algebras. Here we initiate an investigation into the class tpLMn×m of tense polyadic n × m-valued Łukasiewicz–Moisil algebras. These algebras constitute a generalization of tense polyadic Boolean algebras introduced by Georgescu in 1979, as well as the tense polyadic n-valued Łukasiewicz–Moisil algebras studied by Chiriţă in 2012. Our main result is a representation theorem for tense (...) polyadic n × m-valued Łukasiewicz–Moisil algebras. (shrink)

In 2015, tense n × m-valued Lukasiewicz–Moisil algebras were introduced by A. V. Figallo and G. Pelaitay as an generalization of tense n-valued Łukasiewicz–Moisil algebras. In this paper we continue the study of tense LMn×m-algebras. More precisely, we determine a Priestley-style duality for these algebras. This duality enables us not only to describe the tense LMn×m-congruences on a tense LMn×m-algebra, but also to characterize the simple and subdirectly irreducible tense LMn×m-algebras.

Paraconsistent extensions of 3-valued Gödel logic are studied as tools for knowledge representation and nonmonotonic reasoning. Particularly, Osorio and his collaborators showed that some of these logics can be used to express interesting nonmonotonic semantics. CG’3 is one of these 3-valued logics. In this paper, we introduce Fidel semantics for a certain calculus of CG’3 by means of Fidel structures, named CG’3-structures. These structures are constructed from enriched Boolean algebras with a special family of sets. Moreover, we also show that (...) the most basic CG’3-structures coincide with da Costa–Alves’ bi-valuation semantics; this connection is displayed through a Representation Theorem for CG’3-structures. By contrast, we show that for other paraconsistent logics that allow us to present semantics through Fidel structures, this connection is not held. Finally, Fidel semantics for the first-order version of the logic of CG’3 are presented by means of adapting algebraic tools. (shrink)

The study of the theory of operators over modal pseudocomplemented De Morgan algebras was begun in papers [20] and [21]. In this paper, we introduce and study the class of modal pseudocomplemented De Morgan algebras enriched by a k-periodic automorphism -algebras). We denote by \ the automorphism where k is a positive integer. For \, the class coincides with the one studied in [20] where the automorphism works as a new unary operator which can be considered as a negation. In (...) the first place, we develop an algebraic study of the class of \-algebras; as consequence, we prove the class \-algebras is a semisimple variety and determine the generating algebras. After doing the algebraic study and using these properties, we built two families of sentential logics that we denote with \ and \ for every k. \ is a 1-assertional logic and \ is the degree-preserving logic both associated with the class of \-algebras. Working over these logics, we prove that \ is paraconsistent with respect to the de Morgan negation \, which is protoalgebraic and finitely equivalential but not algebraizable. In contrast, we prove that \ is algebraizable, sharing the same theorems with \, but not paraconsistent with respect to \. Furthermore, we show that \ and \ are paracomplete logics with respect to \ and \ and paraconsistent logics with respecto to \, for every k. (shrink)

In this paper, the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N and O satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to analyze the class of mbC-structures. Thus, substructures, union (...) of chains, direct products, direct limits, congruences and quotient structures can be analyzed under this perspective. In particular, a Birkhoff-like representation theorem for mbC-structures as subdirect products in terms of subdirectly irreducible mbC-structures is obtained by adapting a general result for first-order structures due to Caicedo. Moreover, a characterization of all the subdirectly irreducible mbC-structures is also given. An alternative decomposition theorem is obtained by using the notions of weak substructure and weak isomorphism considered by Fidel for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_n$$\end{document}-structures. (shrink)

Multialgebras (or hyperalgebras) have been very much studied in the literature. In the realm of Logic, they were considered by Avron and his collaborators under the name of non-deterministic matrices (or Nmatrices) as a useful semantics tool for characterizing some logics (in particular, several logics of formal inconsistency or LFIs) which cannot be characterized by a single finite matrix. In particular, these LFIs are not algebraizable by any method, including Blok and Pigozzi general theory. Carnielli and Coniglio introduced a semantics (...) of swap structures for LFIs, which are Nmatrices defined over triples in a Boolean algebra, generalizing Avron's semantics. In this paper we develop the first steps towards the possibility of defining an algebraic theory of swap structures for LFIs, by adapting concepts of universal algebra to multialgebras in a suitable way. (shrink)

In situations where we ignore everything but the space of possibilities, we ought to suspend judgment—that is, remain agnostic—about which of these possibilities is the case. This means that we cannot sum our degrees of belief in different possibilities, something that has been formalized as an axiom of non-additivity. Consistent with this way of representing our ignorance, I defend a doxastic norm that recommends that we should nevertheless follow a certain additivity of possibilities: even if we cannot sum degrees of (...) belief in different possibilities, we should be more confident in larger groups of possibilities. It is thus shown that, in the type of situation considered (in so-called ‘classical ignorance’, i.e. “behind a thin veil of ignorance”), it is epistemically rational for advocates of suspending judgment to endorse this comparative confidence; while on the other hand it is shown that, even in classical ignorance, no stronger belief—such as a precise uniform probability distribution—is warranted. (shrink)

It is not uncommon in the history of science and philosophy to encounter crucial experiments or crucial objections the truth-value of which we are ignorant, that is, about which we suspend judgment. Should we ignore such objections? Contrary to widespread practice, I show that in and only in some circumstances they should not be ignored, for the epistemically rational doxastic attitude is to suspend judgment also about the hypothesis that the objection targets. In other words, suspension of judgment “propagates” from (...) the crucial objection to the hypothesis. In this paper I study under which conditions this phenomenon occurs, and discuss its significance for the topics of skepticism, scientific realism, and peer disagreement. (shrink)

Involutive Stone algebras were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued Łukasiewicz–Moisil algebras. In this work we focus on the logic that preserves degrees of truth associated to S-algebras named Six. This follows a very general pattern that can be considered for any class of truth structure endowed with an ordering relation, and which intends to exploit many-valuedness focusing on the notion of inference that results from preserving lower bounds of truth values, and (...) hence not only preserving the value $1$. Among other things, we prove that Six is a many-valued logic that can be determined by a finite number of matrices. Besides, we show that Six is a paraconsistent logic. Moreover, we prove that it is a genuine Logic of Formal Inconsistency with a consistency operator that can be defined in terms of the original set of connectives. Finally, we study the proof theory of Six providing a Gentzen calculus for it, which is sound and complete with respect to the logic. (shrink)

El término nuestroamericano —utilizado por Horacio Cerutti— tiene sus fundamentos en el concepto "Nuestra América". Este hilo conductor de pensamiento tiene como hecho ineludible el hacerse cargo de la realidad en que se vive y del lugar en donde se está, hecho expresado en un permanente interés en la identidad cultural y nacional, como también por una lectura crítica y explicativa del desarrollo de las ideas. En el caso de Chile, a nuestro juicio, la memoria filosófica nuestroamericana ha tendido a (...) ser borrada, olvidada, siendo obnubilada por un fuerte eurocentrismo, lo que ha dado como resultado un escaso número de filósofos preocupados por "lo latinoamericano". Así, este trabajo indaga sobre los orígenes de la vertiente latinoamericanista en la filosofía chilena en la segunda mitad del siglo XX. A modo de conclusión, proponemos que no es sino hasta los años ochenta cuando, desde el Círculo de Filosofía de la Academia de Humanismo Cristiano, se genera un punto de inflexión con la tradición filosófica chilena, dando origen de forma más nítida a la vertiente nuestroamericana que, antes de esto, solo habría tenido pequeñas huellas dispersas. (shrink)

El presente artículo interroga de la naturaleza semiótica de la educación inclusiva y sus problemas de regulación ontológicos, visuales y epistémicos. Este problema comienza a evidenciarse cuando, buena parte, de la consciencia heurística de la educación especial se toma literalmente como la lengua natural de un espacio intelectual en blanco pero altamente generador en la transformación del conocimiento pedagógico. Tal transferencia, devino en la cristalización de un modelo semiótico universal que alcanza su efectividad a través de la castración de la (...) identidad semiológica de lo inclusivo, lo que afianza un sistema de edipización de sus signos y, con ello, coloca de manifestando un sistema de desviación sobre sus propiedades ontológicas implícitas. Producto de esta operación, es que, sus diferentes tipos de agenciamientos de enunciación son objeto de confusión y tervigersación, especialmente, sobre sus unidades semiológicas auténticas. Estamos en presencia de una operación estratégicamente intencionada que contribuye a castrar la pregunta por los signos de lo inclusivo y, por consiguiente, a instalar un sistema de edipización sobre su objeto. El método empleado es el de revisión documental crítica. El trabajo concluye que, al imponer el rostro de la educación especial como parte del corazón de la educación inclusiva se omite la intención de colocar en conexión sus dos tipos de representaciones, las que, también pueden ser interpretadas como formaciones particulares del poder, por medio de las cuales, se designa un modo particular de funcionamiento que es afianzado a través de un sistema de descodificación generalizada de sus signos y flujos semióticos. (shrink)

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of "non-existing" objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non (...) unlike the notion of "truth at world" found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization). (shrink)

INTRODUZIONE 2 1. POVERA E NUDA VAI, FILOSOFIA… 19 1.1 TRA SCIAMANI E CALCOLATORI 20 1.2 AUTOCASTRAZIONI E DINTORNI 25 1.2.1 Debes, ergo potes 26 1.2.1.1 Scienze della natura e scienze dello spirito 27 1.2.1.2 Orizzonti di responsabilità 32 1.2.1.3 Ritrovare la saggezza 36 1.2.2 Potes, ergo debes 37 1.2.2.1 Disintegrando la frammentazione 40 1.2.2.2 Disarticolando lo smembramento 51 1.2.2.3 Oltrepassando l’autosuperamento 58 1.3 IL (MIO) PUNTO DI VISTA 62 2. GLOBALIZZAZIONE E UNIVERSALISMO 70 2.1 PENSARE LA GLOBALIZZAZIONE 73 2.1.1 (...) Una civiltà universale? 73 2.1.1.1 Quale cultura? 74 2.1.1.2 Singolare e plurale 78 2.1.2 Scontro delle civiltà? 85 2.2 CERCANDO UN’ETICA GLOBALE 89 2.2.1 Il minimalismo morale 92 2.2.1.1 Un confronto con il liberalismo neo-contrattualista 96 2.2.1.2 La quercia, la ghianda e la foresta 100 2.2.2 L’etica mondiale 102 2.3 RIFLESSIONI CRITICHE 107 3. RELATIVISMO 112 3.1 LE RAGIONI DEL RELATIVISMO 114 3.1.1 Ragioni della politica 116 3.1.1.1 Multiculturalismo e neutralità etica 116 3.1.1.2 Antifondazionalismo e democrazia 121 3.1.2 Ragioni dell’antropologia 125 3.1.3 Ragioni dell’ermeneutica 130 3.1.4 Ragioni dell’epistemologia 135 3.1.5 Ragioni dell’etica 143 3.1.5.1 Nel regno della necessità 145 3.1.5.2 In regime di cieca obbedienza 146 3.1.5.3 Il piacere e l’interesse 151 3.1.5.4 Intuizioni, emozioni, prescrizioni 153 3.1.5.5 Accordo, consenso e permesso 159 3.1.5.6 Etica della ragione 166 3.2 LA RAGIONE PRATICA 170 3.2.1 Oltre l’ansia cartesiana 171 3.2.2 Autenticità e ragionamento 176 3.2.3 Ragioni della diversità e ragioni del riconoscimento 181 4. FIGURE DI RAZIONALITÀ PRATICA 185 4.1 UTILITARISMO 186 4.1.1 Cosa è «migliore»? 187 4.1.1.1 Piacere, felicità, bene 188 4.1.1.2 L’atto e la regola 191 4.1.2 Conta solo il risultato? 194 4.2 CONTESTUALISMO 197 4.2.1 Recupero della phrónesis 198 4.2.2 Recupero della prâxis 204 4.2.3 Recupero dell’éthos 208 4.3 ETICA DEL DISCORSO 217 4.3.1 Dalle pretese di validità del discorso al principio di un’etica universale 218 4.3.2 Universalità e formalismo 224 4.3.3 Limiti dell’etica del discorso 226 4.4 ETICA DELLA RELAZIONE 231 4.4.1 Relazione versus rappresentazione 232 4.4.2 L’umanità dell’altro uomo 236 4.5 UN BILANCIO 241 ALCUNE PROSPETTIVE. POSTILLA 245 . (shrink)