The paper aims at studying, in full generality, logics defined by imposing a variable inclusion condition on a given logic $$\vdash $$. We prove that the description of the algebraic counterpart of the left variable inclusion companion of a given logic $$\vdash $$ is related to the construction of Płonka sums of the matrix models of $$\vdash $$. This observation allows to obtain a Hilbert-style axiomatization of the logics of left variable inclusion, to describe the structure of their reduced models, (...) and to locate them in the Leibniz hierarchy. (shrink)

In this paper we investigate AGM belief contraction operators by using the tools of algebraic logic. We generalize the notion of contraction to arbitrary finitary propositional logics, and we show how to switch from a syntactic-based approach to a semantic one. This allows to build a solid bridge between the validity of AGM postulates in a propositional logic and specific algebraic properties of its intended algebraic counterpart. Such a connection deserves particular attention when we deal with maxichoice contractions, as studied (...) in the final part of the paper. (shrink)

The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn as a variation on a time-honoured logical system by C.I. Lewis’ student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is “analytically contained” in its antecedent. DAI has been investigated both proof-theoretically and model-theoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics for DAI, (...) showing their equivalence with the known semantics by Dunn and Epstein. We also show that DAI is algebraisable and we identify its equivalent quasivariety semantics. This class turns out to be a linguistic and axiomatic expansion of involutive bisemilattices, a subquasivariety of which forms the algebraic counterpart of Paraconsistent Weak Kleene logic. This fact sheds further light on the relationship between containment logics and logics of nonsense. (shrink)

In this paper, first, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic ⊢ with a composition term. Then, we investigate their position into the lattice of co...

Paraconsistent weak Kleene logic is the $3$-valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} $. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. This $6$-valued logic, (...) unlike $\textrm{PWK} $, fails to be paraconsistent. We describe its consequence relation via a variable inclusion criterion and identify its Suszko-reduced models. (shrink)

This paper offers a logico-algebraic investigation of AGM belief revision based on the logic of paradox ( \(\mathrm {LP}\) ). First, we define a concrete belief revision operator for \(\mathrm {LP}\), proving that it satisfies a generalised version of the traditional AGM postulates. Moreover, we investigate to what extent the Levi and Harper identities, in their classical formulation, can be applied to a paraconsistent account of revision. We show that a generalised Levi-type identity still yields paraconsistent-based revisions that are fully (...) compatible with the AGM postulates. The main outcome is that, once the classical AGM framework is lifted up to an appropriate level of generality, it still appears as a regulative ideal for treating of paraconsistent-based epistemic operators. (shrink)

Hintikka’s game theoretical approach to semantics has been successfully applied also to some non-classical logics. A recent example is Başkent (A game theoretical semantics for logics of nonsense, 2020. arXiv:2009.10878), where a game theoretical semantics based on three players and the notion of dominant winning strategy is devised to fit both Bochvar and Halldén’s logics of nonsense, which represent two basic systems of the family of weak Kleene logics. In this paper, we present and discuss a new game theoretic semantics (...) for Bochvar and Halldén’s logics, GTS-2, and show how it generalizes to a broader family of logics of variable inclusions. (shrink)

Paraconsistent Weak Kleene Logic is the 3-valued propositional logic defined on the weak Kleene tables and with two designated values. Most of the existing proof systems for PWK are characterised by the presence of linguistic restrictions on some of their rules. This feature can be seen as a shortcoming. We provide a cut-free calculus for PWK that is devoid of such provisos. Moreover, we introduce a Priest-style tableaux calculus for PWK.

The paper studies the containment companion of a logic \. This consists of the consequence relation \ which satisfies all the inferences of \, where the variables of the conclusion are contained into those of the set of premises, in case this is not inconsistent. In accordance with the work started in [10], we show that a different generalization of the Płonka sum construction, adapted from algebras to logical matrices, allows to provide a matrix-based semantics for containment logics. In particular, (...) we provide an appropriate completeness theorem for a wide family of containment logics, and we show how to produce a complete Hilbert style axiomatization. (shrink)

The aim of this article is to discuss pure variable inclusion logics, that is, logical systems where valid entailments require that the propositional variables occurring in the conclusion are included among those appearing in the premises, or vice versa. We study the subsystems of Classical Logic satisfying these requirements and assess the extent to which it is possible to characterise them by means of a single logical matrix. In addition, we semantically describe both of these companions to Classical Logic in (...) terms of appropriate matrix bundles and as semilattice-based logics, showing that the notion of consequence in these logics can be interpreted in terms of truth (or non-falsity) and meaningfulness (or meaninglessness) preservation. Finally, we use Płonka sums of matrices to investigate the pure variable inclusion companions of an arbitrary finitary logic. -/- . (shrink)

Bochvar algebras consist of the quasivariety $\mathsf {BCA}$ playing the role of equivalent algebraic semantics for Bochvar (external) logic, a logical formalism introduced by Bochvar [4] in the realm of (weak) Kleene logics. In this paper, we provide an algebraic investigation of the structure of Bochvar algebras. In particular, we prove a representation theorem based on Płonka sums and investigate the lattice of subquasivarieties, showing that Bochvar (external) logic has only one proper extension (apart from classical logic), algebraized by the (...) subquasivariety $\mathsf {NBCA}$ of $\mathsf {BCA}$. Furthermore, we address the problem of (passive) structural completeness ((P)SC) for each of them, showing that $\mathsf {NBCA}$ is SC, while $\mathsf {BCA}$ is not even PSC. Finally, we prove that both $\mathsf {BCA}$ and $\mathsf {NBCA}$ enjoy the amalgamation property (AP). (shrink)

Logics of significance have been proposed in an attempt to overcome the shortcomings of classical logic as a model of reasoning in the presence of nonsignificant (e.g., meaningless, ill-formed, unverifiable) sentences. Many-valued logicians have addressed this problem by introducing logics with infectious truth values. Cases in point are the weak Kleene logics B3 (paracomplete weak Kleene logic) and PWK (paraconsistent weak Kleene logic). Over time, it has become clear that the valid entailments of these significance logics obey variable inclusion patterns (...) that link them to other, usually better known, logics—such patterns, however, allow for disturbing exceptions. Logics of pure (left or right) variable inclusion have been introduced with an eye to removing these exceptions. In this paper, we consider the pure left variable inclusion companion of classical logic and give a complete description of its subclassical extensions. We also provide relative axiomatizations and characteristic (sets of) matrices for each one of these extensions, as well as syntactic descriptions (in terms of variable inclusion criteria) for the valid entailments of some of them, and determine in each case the algebra reducts of the Suszko-reduced matrix models. (shrink)

High-level improvising musicians master idiosyncratic gesture vocabularies that allow them to express themselves in unique ways. The full use of such vocabularies is nevertheless challenged when improvisers incorporate electronics in their performances. To control electronic sounds and effects, they typically use commercial interfaces whose physicality is likely to limit their freedom of movement. Based on Jim Black's descriptions of his ideal digital musical instrument, embodied improvisation gestures, and stage performance constraints, we develop the concept of a modular wearable MIDI interface (...) to closely meet the needs of professional improvisers, rather than proposing a new generic instrument that would require substantial practice to adapt improvisational techniques already acquired. Our research draws upon different bodies of knowledge, from theoretical principles on collaboration and embodiment to wearable interface design, in order to create a digital vest called Track It, Zip It that features two innovative on-body sensors. Allowing for sound control, these sensors are seamlessly integrated with Black's improvisational gesture vocabulary. We then detail the design process of three TIZI prototypes structured by the outcomes of a performance test with Black, a public performance by a novice improviser during the 2017 International Guthman Musical Instrument Competition, and measurements of sensor responses. After commenting on the strengths and weaknesses of the final TIZI prototype, we discuss how our interdisciplinary and collective process involving a world-class improviser at the very center of the design process can provide recommendations to designers who wish to create interfaces better adapted to high-level performers. Finally, we present our goals for the future creation of a wireless version of the vest for a female body based on Diana Policarpo's artistic vision. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Collection of parables on Jaina ethics; based on the Jaina Agamas.

Comparative study of the fundamentals of Sankhya philosophy in comparison of other schools of Indic philosophy.

Juan B. Justo en la historia y el pensamiento argentinos, por A. Solari.--Teoría y práctica de la historia, por M. H. Alberti.--La base biológica de la historia, por F. Escardó.--La técnica, por A. Justo.--La economía, por R. Bogliolo.--La guerra, por A. G. Rodríguez.--La política, por A. Ghioldi.--La lucha de ciases, por R. Mondolfo.--El salariado, por M. Palacín.--Las formas típicas del privilegio, por J. L. Pena.--El gremialismo proletario, por E. Frugoni.--La cooperación libre, por N. Repetto.--La democracia obrera, por L. Pan.--La religión, (...) la cilencia, el arte, por R. Rivière. (shrink)

“Para que isso servirá em minha vida?” Ao longo de minha trajetória como professor do ensino secundário, ouvi esta pergunta algumas vezes. É provável que nós professores de filosofia não sejamos um alvo privilegiado dessa pergunta provocadora. Trata-se mesmo de uma questão legítima, ainda mais para nós: latinoamericanos, brasileiros, nordestinos, piauienses. Trata-se de uma pergunta que evoca um certo desespero, uma certa pressa, um tipo de agonia que é bem nossa; como quando dizemos “estou agoniado”. Queremos tudo “pra já”. Parece (...) que jamais nos daremos o direito de viver e aprender algo pelo simples fato de que o saber é bom e merece ser fruído. (shrink)

Collection of fundamentals text of the six systems of Hindi philosophy.

Of Peter Abelard's logical writings, the fruit of thirty-five years of his activity as a teacher and dialectician, there have been to date only four editions worthy of note: that of Cousin in 1836, of Geyer in 1919 and 1936, of Dal Pra in 1954, and lastly the critical reconstruction of Abelard's literal glosses by L. M. Rijk in 1956. With this handsome second edition of minor but relevant glosses of Abelard, Dal Pra aims to fill the gap still existing (...) in the previous collections. His volume includes Abelard's writings found in the Paris BN manuscripts n. 13.368 and 7493. Chronologically the former belongs to the period when Abelard was given the chair of dialectic at the University of Paris in 1114 and the latter to Abelard's more mature period when he began original speculations on the logical status of propositions in 1121. Dal Pra argues at great length that the glosses in the first manuscript are to be read as the best and only introduction to Abelard's own work on dialectic. Hence he suggests against Rijk the title Introductiones Dialecticae rather than Introductiones Parvulorum. He assembles them according to what he believes was Abelard's intellectual development at the time. They are: the glosses to Porphyrius, to Aristotle's Categories, to the De Interpretatione, and to Boethius' De Devisione. [[sic]] The second section of the volume contains the glosses Super Topica where Abelard discusses among other subjects his first position on the problem of universals. Against Geyer who had consigned these works to the literal glosses of Abelard, Dal Pra offers strong evidence for locating them in the bulk of Abelard's De Ingredientibus precisely between the De Interpretatione and the De Syllogismo Hypothetico. The modernity of Abelard's logical theory is well known among contemporary logicians. Dal Pra's finely planned and handsomely executed edition makes an excellent contribution to the history of medieval logic as well as to contemporary logical theories on names and propositions.--L. M. P. (shrink)

On Hindu ethics and religious life of India as depicted in Nirukta of Yāska, 7th century commentary on Nighaṇṭu, thesaurus of Vedic synonyms.

Articles on different religious philosophies of pre-colonial Bengal, India.