In this book, the authors introduce the linguistic set associated with a linguistic variable and the structure of matrices, which they define as linguistic matrices. The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set. This book is organised into three chapters. The first chapter is introductory, in which we introduce all the basic concepts of linguistic variables and the associated linguistic set to make this book self-contained. (...) Chapter two introduces linguistic matrices and develops basic properties associated with them, like types of matrices, transpose of matrices and diagonal matrices. Most of the properties enjoyed by real or complex matrices are satisfied by these linguistic matrices. Chapter three deals with operations on the linguistic matrices. (shrink)

In the present paper, we study some properties of matrices for non-structural consequence operators. These matrices were introduced in a former work (see [3]). In sections 1. and 2., general definitions and theorems are recalled; in section 3. a correspondence is studied, among our matrices and Wójcicki's ones for structural operators. In section 4. a theorem is given about operators, induced by submatrices or epimorphic images, or quotient matrices of a given one.Such matrices are used (...) to characterize lattices of non-structural consequence operators, by constructing lattices, antiisomorphic to them (see section 5.). In the last section, a sufficient condition is given for a non-structural operator to be finite. (shrink)

We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.

It is well documented that training the rules employed in figural matrices tests enhances test performance. Previous studies only compare experimental conditions in which all or no rules were trained and therefore ignore the particular influence of knowledge about the easy and difficult rules. With the current study, we wanted to provide some first insights into this topic. Respondents were assigned to four groups that received training for no rules, only the easy rules, only the difficult rules, or for (...) all rules. The results show that a training only for the difficult rules was more effective than the other trainings. This applies also to performance in the easy rules that were actually not part of the training. A possible explanation for this finding is a facilitation of the solution process that is primarily driven by knowledge about the difficult rules. In conclusion, our results demonstrate that taking differences between the rules into account may provide a deeper understanding of the effects of trainings for figural matrices tests. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:American Journal of Philology 123.1 (2002) 119-122 [Access article in PDF] Mary Depew and Dirk Obbink, eds. Matrices of Genre: Authors, Canons, and Society. Center for Hellenic Studies Colloquia 4. Cambridge, Mass.: Harvard University Press, 2000. vi + 346 pp. Cloth, $50. The present collection of essays, which originated as a colloquium at the Center for Hellenic Studies, starts, in the words of editor and organizer Dirk Obbink, (...) from the premise that "genre is a conceptual orienting device that suggests to the hearer the sort of receptorial conditions in which a fictive discourse might have been delivered." Obbink goes on to note that, as the discussion at the colloquium developed, "a more text-based conception of authorial performance" began to emerge (6). This evolution in turn parallels the movement in the volume from an initial discussion of archaic and classical Greek genres to those of Hellenistic poetry and its Roman imitators. One can only applaud this attempt to provide a more sophisticated framework for the reading and reception of ancient literature. As befits the stature of the sponsoring institution and of the many distinguished participants, all the contributions are of an unquestionable competence. In the end, however, it is unclear that we have achieved a more complex, refined, or problematized concept of genre than that with which we began. Indeed, with a few exceptions, most of the modern debates about the concept of genre are either ignored or cited in passing rather than directly engaged. Nonetheless, there are a number of interesting and important individual papers in this volume and only a few that disappoint.Among the most praiseworthy is Eric Csapo's "From Aristophanes to Menander? Genre Transformation in Greek Comedy." Csapo takes dead aim at the traditional narrative of the evolution from a politically engaged Old Comedy of ribald invective to an apolitical plot-centered New Comedy typified by Menander and his Roman epigones. Csapo's argument is that this narrative was manufactured, not through the accidents of preservation, but through a deliberate selection and canonization of texts by early Peripatetic critics and scholars. When we characterize Old Comedy as being typified by Aristophanes' carnivalesque assaults on the Athenian political establishment and then point to his plays as proof, we are not only engaging in circular reasoning, we are also treading a path that has been deliberately and tendentiously drawn for us. Thus, while the traditional narrative depicts a linear evolution from iambic to Old Comedy to New Comedy, which is portrayed as a movement from the personal and the topical to the universal and the apolitical, Aristotle himself, as Csapo notes (117), admits that Crates, Aristophanes' predecessor, abandoned the iambic and began to compose generalizing plots (Po. 1449b7-8). In short, plots of the kind deemed [End Page 119] typical of New Comedy are to be found at the very beginning of the comic form. By the same token, we have evidence of political comedy surviving well past Aristophanes' supposed invention of the Middle Comic style in the Plutus. Indeed, the last example of an Athenian comedy of political invective is Demetrius' Areopagite, dating from circa 294 B.C.E.Csapo's argument, of course, is not a simpleminded refusal to acknowledge change but rather an attempt to rethink the historical evolution of the comic genre outside the bounds of a narrow, teleological narrative. Genres are always complex negotiations between competing conceptions of the same form by different producers and consumers. At various times, for various intrinsic and extrinsic reasons, different versions of the same form will be ascendant or fading into eclipse. But it is never a question of an essence that either unfolds its fullness over time or declines from a single ideal instantiation.Less revolutionary but equally persuasive is Joseph W. Day's "Epigram and Reader: Generic Force as (Re-)Activation of Ritual." Day examines the relation between dedicatory epigrams on cult statues and their ritual contexts by arguing that the dedicatory genre is essentially performative rather than constative. These epigrams do their social work by activating a performative context in the mind of the reader... (shrink)

The main result of the present paper — Theorem 3 — establishes the equivalence of the interpolation and amalgamation properties for a large family of logics and their associated classes of matrices.

The plurivalent logics considered in Graham Priest's recent paper of that name can be thought of as logics determined by matrices whose underlying algebras are power algebras, where the power algebra of a given algebra has as elements textit{subsets} of the universe of the given algebra, and the power matrix of a given matrix has has the power algebra of the latter's algebra as its underlying algebra, with its designated elements being selected in a natural way on the basis (...) of those of the given matrix. The present discussion stresses the continuity of Priest's work on the question of which matrices determine consequence relations which remain unaffected on passage to the consequence relation determined by the power matrix of the given matrix with the corresponding question in equational logic as to which identities holding in an algebra continue to hold in its power algebra. Both questions are sensitive to a decision as to whether or not to include the empty set as an element of the power algebra, and our main focus will be on the contrast, when it is included, between the power matrix semantics and the four-valued Dunn--Belnap semantics for first-degree entailment a la Anderson and Belnap) in terms of sets of classical values, in which the empty set figures in a somewhat different way, as Priest had remarked his 1984 study, `Hyper-contradictions', in which what we are calling the power matrix construction first appeared. (shrink)

The paper is a continuation of the investigations of [3]. We assume that the reader is familiar with the notion of an !-saturated model and the notation applied in the theory of models. We refer to [2] for all model- theoretic terms which appear in this note.

Ce volume est la première étape dans la question philosophique de l'existence de Dieu. Qu'est-ce qu'être intelligent sinon la capacité de rechercher et de recevoir la vérité? Il y a plus : la raison peut conduite à la fois, à Dieu. Et même, l'acte de foi est essentiellement un acte d'intelligence. La connaissance de Dieu vivifie la raison et la couronne. L'intelligence a été donnée par Dieu à l'homme et, avec elle, les idées dont l'être est l'âme et Dieu l'intelligence (...) suprême. (shrink)

Sections 1, 2 and 3 contain the main result, the strong finite axiomatizability of all 2-valued matrices. Since non-strongly finitely axiomatizable 3-element matrices are easily constructed the result reveals once again the gap between 2-valued and multiple-valued logic. Sec. 2 deals with the basic cases which include the important F i from Post's classification. The procedure in Sec. 3 reduces the general problem to these cases. Sec. 4 is a study of basic algebraic properties of 2-element algebras. In (...) particular, we show that equational completeness is equivalent to the Stone-property and that each 2-element algebra generates a minimal quasivariety. The results of Sec. 4 will be applied in Sec. 5 to maximality questions and to a matrix free characterization of 2-valued consequences in the lattice of structural consequences in any language. Sec. 6 takes a look at related axiomatization. problems for finite algebras and matrices. We study the notion of a propositional consequence with equality and, among other things, present explicit axiomatizations of 2-valued consequences with equality. (shrink)

ABSTRACTThe articles Maximality and Refutability Skura [. Maximality and refutability. Notre Dame Journal of Formal Logic, 45, 65–72] and Three-valued Maximal Paraconsistent Logics Skura and Tuziak [. Three-valued maximal paraconsistent logics. In Logika. Wydawnictwo Uniwersytetu Wrocławskiego] introduced a simple method of proving maximality of a given paraconsistent matrix. This method stemmed from the so-called refutation calculus, where the focus in on rejecting rather than accepting formulas. The article A Generalisation of a Refutation-related Method in Paraconsistent Logics Trybus [. A generalisation (...) of a refutation-related method in paraconsistent logics. Logic and Logical Philosophy, 27. doi:10.12775/llp.2018.002] was a first step towards generalising the method. In it, a number of 3-valued paraconsistent matrices were shown maximal. In this article we extend these results to cover a number of n-valued paraconsistent matrices using the same method. (shrink)

We show that base matrices for P(ω)∕fin of regular height larger than h necessarily have maximal branches that are not cofinal. The same holds for base matrices of height h if tSpoiler

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A possible world semantics for standard modal languages is presented, where the valuation functions are allowed to be partial, the truth--functional connectives are interpreted according to weak Kleene matrices, and the necessity operator is given a "weak" interpretation. Completeness and incompleteness results for some (axiomatic) systems are then established. Extensions of these modal logics in which figure "statability" operators are also examined.

It is shown that the class of reduced matrices of a logic is a 1 st order -class provided the variety associated with has the finite replacement property in the sense of [7]. This applies in particular to all 2-valued logics. For 3-valued logics the class of reduced matrices need not be 1 st order.

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. This book will be highly useful to social scientists who wish (...) to work with multi expert models. (shrink)

In this book authors study neutrosophic super matrices. The concept of neutrosophy or indeterminacy happens to be one the powerful tools used in applications like FCMs and NCMs where the expert seeks for a neutral solution. Thus this concept has lots of applications in fuzzy neutrosophic models like NRE, NAM etc. These concepts will also find applications in image processing where the expert seeks for a neutral solution.

In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of a class of logical matrices. (...) In this way, any logic verified by an actual matrix in one of these classes has the property the class generally represents. Particular matrices (and so, logics) in each class are provided. (shrink)

Viale introduced covering matrices in his proof that SCH follows from PFA. In the course of the proof and subsequent work with Sharon, he isolated two reflection principles, CP and S, which, under certain circumstances, are satisfied by all covering matrices of a certain shape. Using square sequences, we construct covering matrices for which CP and S fail. This leads naturally to an investigation of square principles intermediate between □κ and □ for a regular cardinal κ. We (...) provide a detailed picture of the implications between these square principles. (shrink)

Résumé L’article vise à souligner la signification politique de l’avènement de la Critique kantienne. Pour ce faire, une double thèse est défendue : il y a une matrice juridique sous-jacente au mouvement conceptuel de la philosophie critique, dont la puissance émancipatrice et révolutionnaire se manifeste à la lumière du contexte historique de sa formulation. L’argument se déploie de la façon suivante : une exploration des rapports entre la formule « révolution de la pensée » que l’on trouve dans la Critique (...) de la raison pure et le contexte historique de la publication l’œuvre ; ensuite un examen de la métaphore juridique et la façon dont elle incarne l’idée d’une philosophie critique ; et pour conclure la suggestion d’une hypothèse interprétative d’après laquelle le « contrat originaire » est un opérateur conceptuel accomplissant un mouvement analogue à celui qui est exigé de la philosophie critique : le passage du niveau individuel au niveau intersubjectif.The aim of the article is to highlight the political significance of the advent of Kant’s Critique. In order to establish it, a double thesis is defended: there is a juridical matrix underlying the conceptual movement of the critical philosophy, whose emancipatory and revolutionary strength is revealed in the light of the context of its formulation. The argument will be deployed in the following way: an exploration of the connections between the formula “a revolution in thought” articulated in the Critique and the historical context of its publication; followed by an exam of the juridical metaphor of the Tribunal and the way in which it embodies the idea of a critical philosophy and finally, as a conclusion, the suggestion of an interpretative hypothesis according to which the notion of contract is a conceptual operator accomplishing an analogous movement to the one required from the critical philosophy: the passage from the subjective level to the intersubjective one. (shrink)

We show by way of example how one can provide in a lot of cases simple modular semantics for rules of inference, so that the semantics of a system is obtained by joining the semantics of its rules in the most straightforward way. Our main tool for this task is the use of finite Nmatrices, which are multi-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set (...) of options. The method is applied in the area of logics with a formal consistency operator (known as LFIs), allowing us to provide in a modular way effective, finite semantics for thousands of different LFIs. (shrink)

We study the matrices, reduced matrices and algebras associated to the systems SAT of structural annotated logics. In previous papers, these systems were proven algebraizable in the finitary case and the class of matrices analyzed here was proven to be a matrix semantics for them.We prove that the equivalent algebraic semantics associated with the systems SAT are proper quasivarieties, we describe the reduced matrices, the subdirectly irreducible algebras and we give a general decomposition theorem. As a (...) consequence we obtain a decision procedure for these logics. (shrink)

One of the generalizations of R. W´ojcicki’s concept of referential matrix is so-called pseudo-referential matrix . G. Malinowski, who introduced that concept, also considers a particular case of pseudo-referential matrices called discrete pseudo-referential matrices . In this note we want to show how any generalized matrix determines a semantically equivalent discrete pseudo-referential matrix.

The main result of the present article is the following: Let N be an infinite subset of,, and let be a matrix with infinitely many rows of completely Ramsey subsets of such that for every n,. Then there exist, a sequence of nonempty finite subsets of N, and an infinite subset T of such that for every infinite subset I of. We also give an application of this result to partitions of an uncountable analytic subset of a Polish space X (...) into sets belonging to the σ‐algebra generated by the analytic subsets of X. (shrink)

This paper introduces and studies hypo-EP matrices of adjointable operators on Hilbert C ∗ -modules, based on the generalized Schur complement. The necessary and sufficient conditions for some modular operator matrices to be hypo-EP are given, and some special circumstances are also analyzed. Furthermore, an application of the EP operator in operator equations is given.

The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Landé's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated (...) in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n!-space is surjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices. (shrink)

There are exactly two nonfinitely axiomatizable algebraic matrices with one binary connective o such thatx(yz) is a tautology of . This answers a question asked by W. Rautenberg in [2], P. Wojtylak in [8] and W. Dziobiak in [1]. Since every 2-element matrix can be finitely axiomatized ([3]), the matrices presented here are of the smallest possible size and in some sense are the simplest possible.

Ordinary dialogical logic offers processing memory as a history of dialogues. Find a reference in this history is an ambiguous process, which can transform in complex or impossible issues the questions that compose a dialogue. Thus, two researches of justifications overlap in a dual problem of justification. In addition, this consideration of the memory uses a lot of technical resources.We propose a dialogical formalism that solves these problems: double justification, composition, memory saving. To do this, we will develop "special" rules (...) that will reconfigure the formalism and consider the metaphysical and philosophical concepts in this logical system and its interpretations.This article is divided into three parts:A presentation of the dialogical framework oriented towards the presentation of the problem of double justification.A re-interpretation of this framework in terms of matrices: the logical formulas modeled on the linguistic and mathematical language reading are replaced by a concept borrowed from the game semantical approach.A brief summary of the new approaches presented by this method: reaffirmation of the clear separation between different levels of analysis and economy on the amount of memory required. (shrink)

Two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. Usually, this theory is presented in an informal manner. In this thesis, I take first steps in formalizing it, and use the formalization to present some considerations in favor of two-dimensional semantics. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that (...) captures the relevant ideas of two-dimensional semantics. I use this to show that some criticisms of two-dimensional semantics that claim that the theory is incoherent are not justified. I also axiomatize the logic, and compare it to the most important proposals in the literature that define similar logics. To indicate that two-dimensional semantics is a plausible semantic theory, I give an argument that shows that all theorems of the logic can be philosophically justified independently of two-dimensional semantics. (shrink)

In this paper we extend some techniques from the theory of conse- quences operations and logical matrices into the wider area of entailment relations.

Let ℋ be a finite-dimensional complex Hilbert space and D the set of density matrices on ℋ, i.e., the positive operators with trace 1. Our goal in this note is to identify a probability measure u on D that can be regarded as the uniform distribution over D. We propose a measure on D, argue that it can be so regarded, discuss its properties, and compute the joint distribution of the eigenvalues of a random density matrix distributed according to (...) this measure. (shrink)

This paper outlines a critique of the use of the genetic variance–covariance matrix (G), one of the central concepts in the modern study of natural selection and evolution. Specifically, I argue that for both conceptual and empirical reasons, studies of G cannot be used to elucidate so-called constraints on natural selection, nor can they be employed to detect or to measure past selection in natural populations – contrary to what assumed by most practicing biologists. I suggest that the search for (...) a general solution to the difficult problem of identifying causal structures given observed correlation’s has led evolutionary quantitative geneticists to substitute statistical modeling for the more difficult, but much more valuable, job of teasing apart the many possible causes underlying the action of natural selection. Hence, the entire evolutionary quantitative genetics research program may be in need of a fundamental reconsideration of its goals and how they correspond to the array of mathematical and experimental techniques normally employed by its practitioners. (shrink)

The class Matr(C) of all matrices for a prepositional logic (, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matr(C) states the following. Assume C to be the consequence operation on a prepositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of C. Then Matr (C) is the (...) least class of matrices containing K and closed under m-reduced products, submatrices, matrix homomorphisms, and matrix homomorphic counter-images. (shrink)

This paper attempts to put some order among the different notions of pain that are to be found in the Nietzschean philosophical corpus. It tries to show that there is a mutation of the Nietzschean concept of pain, from the notion of pain as evaluation to that of pain as localization of a commotion. Therefore pain is not in itself the source of a reaction, but is actually a consequence of a commotion that a reaction has already addressed by the (...) time of the appearance of pain. A deeper notion of pain is therefore sketched here, one that depicts it as an illusory reaction, destined at separating the global commotion of the organism from its alleged localized cause, thus separating the action from the agent and postponing the facing of the global effect of the commotion. It is for this reason that pain becomes a kind of “matrix” for the understanding of our interior life for Nietzsche, as well as a philosophical indicator of his theoretical adversaries. Finally, the end of this article attempts to show that certain positive indications for a different status of pain might serve as guiding lines for the uncovering of a Nietzschean theory of action. (shrink)

Sentences describe situations, and from the point of view of pragmatics, the situation described by a sentence depends in turn on the context of use, i.e. on the situation in which the sentence is uttered. In general, situations are abstract imaginary entitles, but some of them do actually hold; these are called facts. If a sentence A uttered in situation a describes a fact, that is, if the situation described by A actually holds in the real world, then A is (...) said to be true . Hence there are at least two ways of defining the meaning of a sentence in pragmatics; first, the meaning of A could be that function from situations into {0, 1} which takes the value l for exactly those situations in which A is true; second, the meaning of A could be that function from situations into situations which, for an argument a, takes the value b exactly in the case when A, if uttered in situation a, describes situation b. (shrink)