Paraconsistent logic from a modal viewpoint
نویسنده
چکیده
In this paper we study paraconsistent negation as a modal operator, considering the fact that the classical negation of necessity has a paraconsistent behavior. We examine this operator on the one hand in the modal logic S5 and on the other hand in some new four-valued modal logics. 2004 Published by Elsevier B.V.
منابع مشابه
Modality and Paraconsistency
Paraconsistent logic was born in the vicinity of modal logic. Moreover, as every other non-classical logicians, paraconsistentists have very often flirted with modalities. The first known system of paraconsistent logic was in fact defined as a fragment of S5, in the late 40s. But a fragment of a modal system is not necessarily a modal system. I will show here, indeed, that Jaśkowski’s D2 is not...
متن کاملParaconsistent Modal Logics
We introduce a modal expansion of paraconsistent Nelson logic that is also as a generalization of the Belnapian modal logic recently introduced by Odintsov and Wansing. We prove algebraic completeness theorems for both logics, defining and axiomatizing the corresponding algebraic semantics. We provide a representation for these algebras in terms of twist-structures, generalizing a known result ...
متن کاملA paraconsistent view on B and S5
Paraconsistent logics are logics that in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we show that the famous modal logics B and S5, can be viewed as paraconsistent logics with several particularly useful properties.
متن کاملModal twist-structures over residuated lattices
We introduce a class of algebras, called twist-structures, whose members are built as special squares of an arbitrary residuated lattice. We show how our construction relates to and encompasses results obtained by several authors on the algebraic semantics of non-classical logics. We define a logic that corresponds to our twist-structures and show how to expand it with modal operators, obtainin...
متن کاملNearly every normal modal logic is paranormal
An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its ne...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Applied Logic
دوره 3 شماره
صفحات -
تاریخ انتشار 2005