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Universal Logic: Evolution of a Project
We discuss the origin and development of the universal logic project. We describe in particular the structure of UNILOG, a series of events created...
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Gentzen-Type Sequent Calculi for Extended Belnap–Dunn Logics with Classical Negation: A General Framework
Gentzen-type sequent calculi GBD+, GBDe, GBD1, and GBD2 are respectively introduced for De and Omori’s axiomatic extensions BD+, BDe, BD1, and BD2 of...
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Pecularities of Some Three- and Four-Valued Second Order Logics
Logics that have many truth values—more than just True and False —have been argued to be useful in the analysis of very many philosophical and...
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Compositional Meaning in Logic
The Fregean-inspired Principle of Compositionality of Meaning (PoC) for formal languages asserts that the meaning of a compound expression is...
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The Pursuit of an Implication for the Logics L3A and L3B
The authors of Beziau and Franceschetto (New directions in paraconsistent logic, vol 152, Springer, New Delhi,
2015 ) work with logics that have the... -
Classical Negation Strikes Back: Why Priest’s Attack on Classical Negation Can’t Succeed
Dialetheism is the view that some true sentences have a true negation as well. Defending dialetheism, Graham Priest argues that the correct account...
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Translating Non-classical Logics into Classical Logic by Using Hidden Variables
Dyadic semantics is a sort of non-truth-functional bivalued semantics introduced in Caleiro et al. (in: Béziau J-Y (ed) Logica Universalis,...
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Sequent Systems for Negative Modalities
Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental...
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N.A. Vasil’ev’s Logical Ideas and the Categorical Semantics of Many-Valued Logic
Here we suggest a formal using of N.A. Vasil’ev’s logical ideas in categorical logic: the idea of “accidental” assertion is formalized with topoi and...
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Liberating Paraconsistency from Contradiction
In this paper we propose to take seriously the claim that at least some kinds of paraconsistent negations are subcontrariety forming operators. We...
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A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes
The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz (modal)...
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Inconsistency-Adaptive Dialogical Logic
Even when inconsistencies are present in our premise set, we can sensibly distinguish between good and bad arguments relying on these premises. In...
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Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility
Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such...
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A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart
Routley–Meyer semantics (RM-semantics) is defined for Gödel 3-valued logic G3 and some logics related to it among which a paraconsistent one...
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Multimodal Incompleteness Under Weak Negations
This paper shows that some classes of multimodal paraconsistent logics endowed with weak forms of negation are incompletable with respect to Kripke...
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Modal Extensions of Sub-classical Logics for Recovering Classical Logic
In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN , CluN and CLaN , in the same way that S0.5 0 extends classical...
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How to Take Advantage of the Blur Between the Finite and the Infinite
In this paper is presented and discussed the notion of true finite by opposition to the notion of theoretical finite. Examples from mathematics and...