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Pure Variable Inclusion Logics
Full text linkThe 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.Fil: Paoli, Francesco. Università Degli Studi Di Cagliari.; ItaliaFil: Pra Baldi, Michele. Università Degli Studi Di Cagliari.; ItaliaFil: Szmuc, Damián Enrique. Universidad de Buenos Aires. Facultad de Filosofía y Letras; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Filosóficas. - Sociedad Argentina de Análisis Filosófico. Instituto de Investigaciones Filosóficas; Argentin
Logics of variable inclusion and the lattice of consequence relations
No full textIn this paper, first, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic (Formula presented.) with a composition term. Then, we investigate their position into the lattice of consequence relations over the language of (Formula presented.)
An algebraic study of logics of variable inclusion and analytic containment
Full text linkThis thesis focuses on a wide family of logics whose common
feature is to admit a syntactic definition based on specific
variable inclusion principles.
This family has been divided into three main components:
logics of left variable inclusion, containment logics, and
the logic of demodalised analytic implication.
We offer a general investigation of such logics within
the framework of modern abstract algebraic logic
Left Variable Inclusion Logics Associated with Classical Logic
Full text linkLogics 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
Algebraic Analysis of Demodalised Analytic Implication
Full text linkThe logic DAI of demodalised analytic implication has been introduced by J.M. Dunn (and independently investigated by R.D. Epstein) 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 (PWK). This fact sheds further light on the relationship between containment logics and logics of nonsense
Percorsi di logica
No full textLo scopo di Percorsi di Logica è guidare il lettore alla scoperta di alcuni tra i temi più importanti della logica formale classica. Il volume mira a esporre in modo rigoroso ed esauriente, agevolando la costruzione di percorsi tematici personalizzati, i concetti e i risultati di base impiegati in questa disciplina, senza trascurarne l’accessibilità da parte di un pubblico non specialista. A tal fine, il testo è corredato di una sezione riservata ai preliminari matematici e alle tecniche dimostrative più comuni. Il volume presenta la logica proposizionale e predicativa, considerandole da una prospettiva semantica e sintattica. Particolare attenzione è riservata alla loro metateoria. Percorsi di Logica è pensato per le esigenze dei nuovi corsi di laurea in discipline umanistiche e scientifiche. Tuttavia, il volume è accessibile anche ai lettori autodidatti che intendono approfondire autonomamente i temi classici e alcuni degli sviluppi più recenti della logica formale
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