Non-Classical Abstract Logics

Non-Classical Abstract Logics

Workshop organized by:

Fabien Schang(National Research Institute, Higher School of Economics, Moscow)

and

James Trafford(University for the Creative Arts at Epsom, London)

Keynote speaker: Joao Marcos
Federal University of Rio Grande do Norte, Brazil


According to the "classical" view, logic is a theory of consequence ,
where Cn is taken to be either a relation between sets of formulas in a
language L or an operator on formulas. By "classical" here, we do not mean
the view of logic which is defined by a semantic model with only two
truth-values (truth and falsity). Rather, we mean the broader sense in which
the foundations of a logic have to do with a basic relation of
truth-preservation. This workshop will question this view, and investigate
alternatives.

There are a number of suggestions available in the literature regarding what
shape such a non-classical "abstract logic" might take. For example, from
the point of view of semantics, Shramko and Wansing suggest a generalized
theory of truth-values and entailment relations which do not solely preserve
truth. From the point of view of dialogue, reasoning and inferentialism, a
number of authors (e.g. Dutilh-Novaes; Restall; Ripley) both investigate the
foundations of logical deduction and question the centrality of
truth-preservation in the construction of logical systems.

We think that there are three predominant attitudes that can be identified
in the investigation of the abstract properties of logical systems. The
first contends that every logical system has ultimately to do with different
ways to preserve truth from premises to conclusion. The second questions the
centrality of truth and makes room for more relations of consequence between
premises and conclusion. Finally, the third is even more radical by
questioning the very relation of consequence. Should the latter always be
seen as a cornerstone in any abstract study of logic? In this vein,
falsification, and relations of rejection, have been studied on a equal
footing with truth-preservation (e.g. Słupecki, Skura). Such investigations
may be understood as initiating a broader view of logical relations that
could lead to a more comprehensive reflection on the discipline. In this
regard, consequence, rejection, inference, or even mere difference (in the
context of a wider reading of the logical concept of opposition) may be
considered to be equally basic notions to investigate the foundations of logic.

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