7/27/2019 salaet
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theory, establishing among others the notions of logical
bi-simplexes (or -structures), of (n-1)-dimensional modal
n(m)-graphs, the logical series of n-
dimensional hyper-flowers and hyper-tetraicosahedra (or
-structures) andthe powerful setting method of modal decoration. In
order to be able to for-malise geometrically (i.e.
n-oppositionally) the existing systems of modal logic(i.e. in order
to show and explore the concrete use and utility of abstract
n-opposition theory as applied to any particular system of modal
logic, normalor non-normal) we need to go beyond this commitment to
graph linearity (forclarity, if the modal graph of S5 is linear,
the one of S4 has two nested fork-ings). We do it in the present
study, where we show how to interpret, insiden-opposition theory,
forkings and isolated points (or isolated basic modalities)
ofclassical and non-classical modal graphs by means of the
set-theoretic decorationmethod newly adapted.
S. Salaet (Barcelona): An abstract algebraic logic view
onNelsons paraconsistent logic N4
The N4 logic is the paraconsistent version of the N3 logic. N3
logic was devel-oped by Nelson in the forties to solve a problem of
the negation in Intuitionisticlogic. The so-called problem of the
strong negation: in the later logic we cantderive the negation of
or from the negation of . In the last years,Odintsov makes a
sistematically study of the variety VN4 which gives complet-ness
for N4. He also characterizes it with help of the socalled
twist-structuresover implicative lattices. We make in relation
these results with the theory ofalgebraic abstrac logic. In
particular we show VN4 gives an algebraic equivalentsemantics to N4
and we also show it is exactly Mod*S, the class of reduced mod-els
of S. This proves N4 is strongly axiomatizable. We also develop an
example
which proves N4 is paraconsistent and not regularly
axiomatizable. Finally weshow special filters, as defined by
Odintsov, are all the filters for every A inVN4.
K. Brunnler (Bern): Is there a proof theory of
temporallogic?
Currently known sequent systems for temporal logics such as
propositional lin-ear time temporal logic (PLTL) either include a
cut rule in some form or aninfinitary rule, which is a rule with
infinitely many premises. Both kinds ofsystems are unsatisfactory
for automated deduction and for studying cut elim-ination. I will
discuss the question of whether there is a satisfactory
finitarycut-free sequent system and what satisfactory means in the
first place.
A. Costa-Leite (Neuchatel): Paraconsistentization of log-ics -
the general theory of paraconsistent logics
Given a logic, how to obtain its paraconsistent counterpart?
Given a paracon-sistent logic, how to obtain the non-paraconsistent
counterpart of this logic?
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