LFIs^15

This is a workshop commemorating the 15 years of the Logics of Formal Inconsistency [◌].

The Logics of Formal Inconsistency (LFIs) are a family of paraconsistent logics that encompasses the majority of paraconsistent systems developed within the Brazilian tradition. In a few words, LFIs have resources to express the notion of consistency inside the object language by means of a sentential unary connective called 'ball', denoted by ◌, and a sentence ◌α is intended to express the meaning that α is consistent.

As in any other paraconsistent logic, explosion does not hold in LFIs. But the vigorous approach of the LFIs allows for the distinction between contradictions that can be accepted from those that cannot. The point of this distinction is that, no matter the nature of the contradictions a paraconsistentist is willing to accept, there are contradictions that cannot be accepted. In the LFIs, negation are explosive precisely with respect to consistent formulas:

◌α, α, ¬α ⊢ β

An LFI is thus a logic that separates the sentences for which explosion holds from those for which it does not hold. The former are marked with ◌. For this reason, they are called gently explosive.

The idea of expressing a kind of “well-behavedness” in the object language is also found in da Costa's C_n hierarchy. In C₁, the consistency of α is expressed by α^◌, and

α, ¬α ⊬ β, while α^◌, α, ¬α ⊢ β

However, in C₁, the well-behavedness of a proposition α is equivalent to saying that α is non-contradictory. What the LFIs have introduced in the literature is a new way of treating consistency, an idea that reveled to be really fruitful.

Although a first step in any paraconsistent logic is the distinction between triviality and contradictoriness, the LFIs permit also the distinction between consistency and non-contradictoriness, as well as contradictoriness and non-consistency. Consistency is not more necessarily regarded as “freedom from contradiction”, but acquires an independent meaning.

We may say, pictorially, that the LFIs are the paraconsistent logics that bravely reintroduce the notion of consistency into the nonclassical picture by neatly balancing the equation:

contradictions + consistency = triviality

The idea that consistency (and inconsistency) may have an independent status in logic and be internalized by way of appropriate logical constants, autonomous from other logical constants such as negation and conjunction, led to a new revival in paraconsistency, with an untold number of applications in areas such as belief revision, formalization of contradictory belief, legal studies, knowledge representation, description logics, probability, quantum computation and linguistics. The present Workhop on the 15 years of the LFIs has the purpose of congregating logicians, philosophers and computer scientists interested in furthering of the research and in the applications of the Logics of Formal Inconsistency, and their unfoldings.

Connections to proof theory, formal semantics, foundations of set theory, model theory other logics and to traditional philosophical topics have also been developed.

Topics of interest to our Workshop include, but are not limited to:

• Logical systems related to LFIs (modal, fuzzy, etc).

• The LFIs and other schools of paraconsistency

• LFIs and computer science

• Possible-translations semantics

• Non-deterministic semantics

• Semantics for LFIs in general

• Proof-theory for LFIs

• Philosophical topics on LFIs

• LFIs and linguistics

• History of paraconsistency

Contributed talks with duration of 25 minutes will be divided into 20 minutes for exposition followed by 5 minutes of discussion. Abstracts should have a minimum of 500 words and a maximum of 1000 words, and should be submitted in a PDF file including relevant information about the authors (name, e-mail address, and scientific affiliation). Submissions and inquiries must be sent to the email meconiglio-AT-gmail.com or walter.carnielli-AT-gmail.com by April 12 (deadline extension: May 1), and the authors will be notified of acceptance or rejection by May 10.

Keynote speakers:

• Arnon Avron, Tel Aviv University

• Talk: "What is a classical LFI, and when are two such logics identical"

• João Marcos, UFRN

• Talk: "On the birth of the LFIs: Some alternative histories"

The workshop chairs are Marcelo Coniglio and Walter Carnielli.

[◌] The birth of the LFIs is here traced back to the II WCP, to the publication of the first paper mentioning "formal inconsistency" in its title, and to the earliest versions of the landmark survey paper containing a proper definition of a Logic of Formal Inconsistency. A later fundamental paper on the topic may be found here.

Be sure to check the full detailed programme of NAT@Logic 2015 here!