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)

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.

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)

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, 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.

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.

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 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...

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 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)

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)

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)

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 lieu of an abstract, here is a brief excerpt of the content:Buddhist-Christian Studies 20 (2000) 265-267 [Access article in PDF] Book Review Community, Violence, and Peace: Aldo Leopold, Mohandas K. Gandhi, Martin Luther King Jr., and Gautama the Buddha in the Twenty-First Century Community, Violence, and Peace: Aldo Leopold, Mohandas K. Gandhi, Martin Luther King Jr., and Gautama the Buddha in the Twenty-First Century. By A. L. Herman. Albany: State University of New York Press, 1998. xi + (...) 245 pp. At first glance, this title might seem a bit over the edge: how could an author intelligently juxtapose such diverse thinkers as an ecological scientist, two advocates of human rights, and an ancient religious founder? For the most part, the author succeeds in demonstrating that the twenty-first century requires a definition of community that includes environmental, social, and spiritual concerns. In a format particularly [End Page 265] helpful for undergraduate teaching, he carefully rehearses at the end of each section three central questions: how does this thinker contribute to our understanding of community? Does his approach lead to the diminishment of violence? Does it facilitate peace?For the first quarter of the book, Herman explores various aspects of community. Drawing from Erich Fromm, Socrates, and Aldous Huxley, he demonstrates that out of enlightened self-interest, all people seek peace for themselves. He is careful to point out, however, that the Socratic virtues of wisdom, courage, self-control, and justice, which arise from within, are far superior to the uniformity of the World State as described in Huxley's Brave New World, which leaves nothing uncontrolled by the external authorities. Both lead to nonviolence and peace, but the World State can fall prey to what Fromm terms cultural insanity.Supplementing his discussion of Aldo Leopold with references to the work of Rachel Carson and J. Baird Callicott, Herman emphasizes that ideas of community peace must be informed by holistic structures of nature, particularly as articulated in Leopold's Sand County Almanac. However, he also warns that if the welfare of the biotic community takes precedence over all other concerns, then society could fall into a state of ecofascism.Herman's chapter on Mahatma Gandhi ably summarizes the life and works of this great political reformer, with particular focus on his formative years in South Africa. Influenced by John Ruskin and Leo Tolstoy, Gandhi developed the concept of the "Ashramic community," a means of collective, intentional living designed to effect social change. After describing the Phoenix Settlement (1904, Johannesburg), the Sabarmati Ashram (1915, Ahmedabad), and Sevagram Ashram (1933, Wardha), Herman presents a fifteen-page play script based on the Asian travel diaries of Professor George P. Conger, chair of philosophy at the University of Minnesota from 1937-1953. Conger spent two months at Gandhi's ashram in Wardha, India, in 1933, and in the play called "Salt," his students take up issues including the ill treatment of Jews in Germany, the definition of nonviolence, and emphasized, as does Gandhi, the necessity for self-transformation to achieve personal and community peace.Martin Luther King Jr. inspired by the example of Mahatma Gandhi, employed nonviolent techniques to bring about the many successes of the American Civil Rights Movement. Herman provides a brief biography of Martin Luther King Jr., quotes several of his pivotal sermons, and emphasizes the notion of beloved community as critical to King's thinking. He writes that "in King's interpretation of agape, it is your being loved that gives you value; and it is your selflessly loving others that gives them value and makes the beloved community possible" (p. 138). According to King, fear and racial discrimination prevent one from entering into the beloved community. By changing laws, and, more importantly, changing the hearts of individual people, a more peaceful community can be built.The least successful chapter of this book discusses Gautama Buddha and the "karmic community." Rather than focusing directly on Buddhist theories of Karma, Herman engages in a long discussion of the Bhagavad Gita, an important Hindu text, as a foil to explain Buddhist theories... (shrink)

Replaces communal altruism with communal egoism as a way of solving problems of too much violence and too little peace in the twenty-first century.

Gadamer's book extends and codifies the main hermeneutical concepts of Bultmann, Heidegger, and their adherents, and can be considered a summa of what Robinson calls "The New Hermeneutic." By Robinson and other theologians, and by Continental literary critics, Wahrheit und Methode has been welcomed as a philosophical justification for "vital and relevant" interpretations that are unencumbered by a concern for the author's original intention. On this point "The New Hermeneutic" reveals its affinities with "The New Criticism" and the newer "Myth (...) Criticism." All three have impugned the author's prerogative to be the determiner of textual meaning. Gadamer, however, grounds his anti-intentionalism only partially in aesthetics and not at all in the collective unconscious but primarily in the radical historicism of Martin Heidegger. (shrink)

The main aim of this article is to offer a sociological concept of crisis that, defined as the expected yet non-lineal outcome of the internal dynamics of modern societies, builds on the synergies between critical theory and systems theory. It contends that, notwithstanding important differences, both traditions concur in addressing crises as a form of self-reproduction of social systems as much as a form of engagement with the complexities and effects of such processes of reproduction. In order to make our (...) comparison exhaustive, this article explores critical and systems theories’ notions of crisis at three levels: (1) their conceptual delimitation of crises; (2) their methodological proposals to empirically observe crises; and (3) their normative attempts to contribute to their resolution. As crises remain a distinctive structural feature of the social world and a rich source of knowledge about it, reflexivity must be seen as a crucial form of engagement with the negative expressions of social life itself. (shrink)

This response to Taylor’s paper, “The Future of Applied Philosophy” (also includ­ed in this issue) describes Taylor’s understanding of the problems that practical philosophy faces; describes Taylor’s responses to these problems, and offers criticisms of his arguments.

The common account of the analog vs digital distinction is based on features of physical systems, being related to the usage of continuous vs discrete supports respectively. It is proposed here to alternatively characterize the concepts of analog and digital as related to coding systems, of which a formal definition is given, by suggesting that the distinction refers to the strategy adopted to define the coding function: extensional in digital systems, isomorphic intensional in analog systems. This thesis is supported by (...) examples, in particular of analog systems exploiting discrete supports, and is discussed to explain why digital coding is currently so widespread in technological and social practice. (shrink)

Introduction -- Defining pluralism : Simon Pokagon, Ida B. Wells-Barnett, and Thomas fortune -- Evolution and American Indian philosophy -- Feminist resistance : Anna Julia Cooper, Jane Addams, and Charlotte Perkins Gilman -- Labor, empire and the social gospel : Washington Gladden, Walter Rauschenbusch, and Jane Addams -- A new name for an old way of thinking : William James -- Making ideas clear : Charles Sanders Peirce -- The beloved community and its discontents : Josiah Royce and the realists (...) -- War, anarchism, and sex : Emma Goldman and Margaret Sanger -- Democracy and social ethics : John Dewey -- Naturalism and idealism, fear, and conventionality : Mary Whiton Calkins and Elsie Clews Parsons -- Race riots and the color line : W. E. B. du Bois -- Philosophy reacts : Hartley Burr Alexander and Morris R. Cohen -- Creative experience : Mary Parker Follett -- Cultural pluralism : Horace Kallen and Alain Locke -- War and the rise of logical positivism : Otto Neurath and Rudolf Carnap -- Mccarthyism and American empiricism : Jacob Loewenberg, Henry Sheffer, C. I. Lewis, and Charles Morris -- The linguistic turn : Gustav Bergmann, May Brodbeck, and W. V. O. Quine -- Resisting the turn : Donald Davidson, Wilfrid Sellars, and the pluralist rebellion -- Philosophy outside : John Muir, Aldo Leopold, Joseph Wood Krutch, and Rachel Carson -- Economics and technology : Lewis Mumford, C. Wright Mills and John Kenneth Galbraith -- Politics : John Rawls, Robert Nozick, Michael Sandel, Martha Nussbaum, and Noam Chomsky -- Civil rights : Martin Luther King, Jr., Richard Wright and James Baldwin -- Black power : Malcolm X, James Cone, Audre Lorde, Bell Hooks, Angela Davis, and Cornel West -- Latin American American philosophy -- Red power, indigenous philosophy : Vine Deloria, Jr. and contemporary American Indian thought -- Feminism -- Engaged philosophy and the environment -- American philosophy today -- Recovering and sustaining the American tradition -- American philosophy revitalized -- The spirit of American philosophy in the new century. (shrink)