Logics of variable inclusion and the lattice of consequence relations

In this paper, firstly, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic L with partition function. Then, we investigate their position into the lattice of consequence relations over the language of L.Comment: arXiv admin note: text overlap with arXiv:1804.08897, arXiv:1809.0676

An algebraic study of logics of variable inclusion and analytic containment

This 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

Pure Variable Inclusion Logics

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.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

An algebraic study of logics of variable inclusion and analytic containment

This 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

Logics of variable inclusion and the lattice of consequence relations

In 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.)

Containment logics: Algebraic Counterparts and Reduced Models

The containment companion of a logic vdash consists of the consequence relation r 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. Following the algebraic analysis started in Bonzio and Pra Baldi (2021, Studia Logica, 109, 969-994), this paper characterizes the algebraic counterpart of a finitary containment logic r and investigates the structure of the Leibniz and Suszko reduced models. The analysis is carried within the framework of abstract algebraic logic.Mathematics Subject Classification: Primary: 03G27. Secondary: 03G2

Proof theory of Paraconsistent Weak Kleene Logic

Paraconsistent Weak Kleene Logic (PWK) 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 (a hybrid between a natural deduction calculus and a sequent calculus) for PWK that is devoid of such provisos. Moreover, we introduce a Priest-style tableaux calculus for PWK

Containment logics: Algebraic Counterparts and Reduced Models

The containment companion of a logic vdash consists of the consequence relation r 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. Following the algebraic analysis started in Bonzio and Pra Baldi (2021, Studia Logica, 109, 969-994), this paper characterizes the algebraic counterpart of a finitary containment logic r and investigates the structure of the Leibniz and Suszko reduced models. The analysis is carried within the framework of abstract algebraic logic.Mathematics Subject Classification: Primary: 03G27. Secondary: 03G2