Completeness and incompleteness for anodic modal logics

Bueno-Soler, Juliana

doi:10.3166/jancl.19.291-310

Cited by 8 publications

(11 citation statements)

References 8 publications

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“…The above sense of consistency ( ) has an essential "possible-world" character. But, as shown in Bueno-Soler [7], many cathodic modal logics can be defined adjoining modal structures on top of LFI's. The main ones are KmbC, KbC and KCi, obtained by extending the LFI's mbC, bC and Ci with the machinery of the modal systems K plus instances of the schema G k,l,m,n .…”

Section: Modal Approaches To Consistency and Inconsistencymentioning

confidence: 99%

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The Single-minded Pursuit of Consistency and its Weakness

Carnielli

2011

Stud Logica

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Saberíamos muito mais das complexidades da vida se nos aplicássemos a estudar com afinco as suas contradições em vez de perdermos tanto tempo com as identidades e coerências, que estas têm obrigação de explicar-se por si mesmas. 1 José Saramago, "A Caverna"Abstract. I argue that a compulsive seeking for just one sense of consistency is hazardous to rationality, and that observing the subtle distinctions of reasonableness between individual and groups may suggest wider, structuralistic notions of consistency, even relevant to re-assessing Gödel's Second Incompleteness Theorem and to science as a whole.

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Section: Modal Approaches To Consistency and Inconsistencymentioning

confidence: 99%

“…A pertinent point here is that the notion of consistency in S2 can be made totally independent of negation. Indeed, consistency (and strict implication) can be defined within the absolutely positive modal logics as in BuenoSoler [7], for ⊃ the material implication:…”

Section: Several Interesting Consequences Followmentioning

confidence: 99%

The Single-minded Pursuit of Consistency and its Weakness

Carnielli

2011

Stud Logica

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“…Kripke semantics for cathodic systems are underlined. The formal treatment for the systems in the class PI k,l,m,n , in particular, is similar to the anodic case, as in [4], with some modifications concerning negation. The other cases, namely mbC k,l,m,n , bC k,l,m,n and Ci k,l,m,n will be treated in more details.…”

Section: Kripke-style Semantic Completenessmentioning

confidence: 99%

Two Semantical Approaches to Paraconsistent Modalities

Bueno-Soler

2010

Log. Univers.

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In this paper we extend the anodic systems introduced in Bueno-Soler (J Appl Non Class Logics 19(3):291-310, 2009) by adding certain paraconsistent axioms based on the so called logics of formal inconsistency, introduced in Carnielli et al. (Handbook of philosophical logic, Springer, Amsterdam, 2007), and define the classes of systems that we call cathodic. These classes consist of modal paraconsistent systems, an approach which permits us to treat with certain kinds of conflicting situations. Our interest in this paper is to show that such systems can be semantically characterized in two different ways: by Kripke-style semantics and by modal possible-translations semantics. Such results are inspired in some universal constructions in logic, in the sense that cathodic systems can be seen as a kind of fusion (a particular case of fibring) between modal logics and non-modal logics, as discussed in Carnielli et al.(Analysis and synthesis of logics, Springer, Amsterdam, 2007). The outcome is inherently within the spirit of universal logic, as our systems semantically intermingles modal logics, paraconsistent logics and manyvalued logics, defining new blends of logics whose relevance we intend to show. Mathematics Subject Classification (2000). Primary 03B45, 03B53; Secondary 03B50, 03B62.

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“…A more intimate relationship between LFIs and their modal versions is investigated by Bueno-Soler in [55], where the so-called anodic modal systems (purely positive modal systems) introduced in [56] are extended by adding certain paraconsistent axioms based on LFIs, defining a class of modal systems called cathodic modal systems. This class consists of modal paraconsistent systems, dealing with certain kinds of conflicting modal situations.…”

Section: Paraconsistent Modalities Consistency and Determinednessmentioning

confidence: 99%

“…a suitable Kripke semantics (see [56]). Observe that these systems are positive, and so they can be used as a basis for modal LFIs, as we shall see below.…”

Section: Paraconsistent Modalities Consistency and Determinednessmentioning

confidence: 99%

LFIs Based on Other Logics

Carnielli

Coniglio

2016

Paraconsistent Logic: Consistency, Contradiction and Negation

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In the previous chapters, all the LFIs studied were based on positive classical logic, CPL + . The basic system considered was mbC, and several extensions of it were proposed. Moreover, we have arrived at several 3-valued logics, most of them algebraizable in the sense of Blok and Pigozzi.In this chapter, we will analyze LFIs defined over other logical bases: positive intuitionistic logic, the four-valued Belnap's logic and some families of fuzzy logics, as well as positive modal logics.

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Completeness and incompleteness for anodic modal logics

Cited by 8 publications

References 8 publications

The Single-minded Pursuit of Consistency and its Weakness

The Single-minded Pursuit of Consistency and its Weakness

Two Semantical Approaches to Paraconsistent Modalities

LFIs Based on Other Logics

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