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Disjoint logics
(Nicolaus Copernicus University, 2021-03-27)
We will present all the mixed and impure disjoint three-valued logics based on the Strong Kleene schema. Some, but not all of them, are (inferentially) empty logics, while one of them is trivial. We will compare them ...
Defining LFIs and LFUs in extensions of infectious logics
(Taylor & Francis, 2016-10)
The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the (¬, ∧, ∨) -fragment of the logics of nonsense, such as the ...
Pure Variable Inclusion Logics
(Uniwersytet Mikołaja Kopernika, 2021-11-28)
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 ...
Completeness for monadic fuzzy logics via functional algebras
(Elsevier Science, 2021-03-01)
We study S5-modal (monadic) expansions of extensions of Hájek's basic logic . Hájek proposed Hilbert-style systems axiomatizing these logics and we prove that completeness theorems for these logics follow from algebraic ...
Hajek's Logic BL and BL-algebras
(College Publications, 2011)
In this chapter we give a detailed presentation of the most important aspects of Hajek´s basic Logic BL and their algebraic counterpart, BL-algebras.
A Note on Goddard and Routley's Significance Logic
(Victoria University of Wellington, 2018-07)
The present note revisits the joint work of Leonard Goddard and Richard Routley on significance logics with the aim of shedding new light on their understanding by studying them under the lens of recent semantic developments, ...
On universality and formality in 19th century symbolic logic: The case of Schröder’s “Absolute Algebra”
(Birkhäuser, 2015)
This paper deals with conceptions of formality underlying 19th Century symbolic logic, where notations and manipulation of signs played an important role. It is devoted specifically to the case of Ernst Schröder’s “formal ...
A family of metainferential logics
(Taylor & Francis, 2019-01)
We will present 12 different mixed metainferential consequence relations. Each one of them is specified using two different inferential Tarskian or non-Tarskian consequence relations: K3, LP, ST or TS+. We will show that ...
Immune Logics
(Victoria University of Wellington, 2021-02)
This article is concerned with an exploration of a family of systems---called immune logics---whose main properties are, in some sense, related to those of the well-known family of infectious logics. The distinctive feature ...
Constructive logic with strong negation as a substructural logic
(Oxford University Press, 2010-08)
Spinks and Veroff have shown that constructive logic with strong negation (CLSN for short), can be considered as a substructural logic. We use algebraic tools developed to study substructural logics to investigate some ...