Paradeduction in Axiomatic Formal Systems

The concept of paradeduction is presented in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, paradeduction is used to show that there is a way to transform any logic, introduced as an axiomatic formal system, into a paraconsistent one

Paraconsistentization and many-valued logics

This paper shows how to transform explosive many-valued systems into paraconsistent logics. We investigate especially the case of three-valued systems showing how paraconsistent three-valued logics can be obtained from them

Conjunctive and Disjunctive Limits: Abstract Logics and Modal Operators

Departing from basic concepts in abstract logics, this paper introduces two concepts: conjunctive and disjunctive limits. These notions are used to formalize levels of modal operators

Definability in Infinitary Languages and Invariance by Automorphisms

Given a $\mathcal L_{\alpha\beta} ^E$-structure $E$, where $\mathcal L_{\alpha\beta} ^E$ is an infinitary language, we show that $\alpha$ and $\beta$ can be chosen in such way that every orbit of the group $G$ of automorphisms of $E$ is $\mathcal L_{\alpha\beta} ^E$-definable. It follows that two sequences of elements of the domain $D$ of $E$ satisfy the same set of $\mathcal L_{\alpha\beta}$-formulas if and only if they are in the same orbit of $G$

Paraconsistent orbits of logics

Some strategies to turn any logic into a paraconsistent system are examined. In the environment of universal logic, we show how to paraconsistentize logics at the abstract level using a transformation in the class of all abstract logics called paraconsistentization by consistent sets . Moreover, by means of the notions of paradeduction and paraconsequence we go on applying the process of changing a logic converting it into a paraconsistent system. We also examine how this transformation can be performed using multideductive abstract logics. To conclude, the conceptual notion paraconsistent orbit of a logic is proposed