27,451 research outputs found
Negation and Dichotomy
The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition
Fredkin Gates for Finite-valued Reversible and Conservative Logics
The basic principles and results of Conservative Logic introduced by Fredkin
and Toffoli on the basis of a seminal paper of Landauer are extended to
d-valued logics, with a special attention to three-valued logics. Different
approaches to d-valued logics are examined in order to determine some possible
universal sets of logic primitives. In particular, we consider the typical
connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As
a result, some possible three-valued and d-valued universal gates are described
which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram
Towards a Proof Theory of G\"odel Modal Logics
Analytic proof calculi are introduced for box and diamond fragments of basic
modal fuzzy logics that combine the Kripke semantics of modal logic K with the
many-valued semantics of G\"odel logic. The calculi are used to establish
completeness and complexity results for these fragments
State/event based versus purely Action or State based Logics
Although less studied than purely action or state based logics, state/event
based logics are becoming increasingly important. Some systems are best studied
using structures with information on both states and transitions, and it is
these structures over which state/event based logics are defined. The logic
UCTL and its variants are perhaps the most widely studied and implemented of
these logics to date. As yet, however, no-one seems to have defined UCTL*, a
trivial step but a worthwhile one. Here we do just that, but prove in the cases
of both UCTL and UCTL* that these logics are no more expressive than their more
commonplace fragments. Also, acknowledging the importance of modal transition
systems, we define a state/event based logic over a modified modal transition
system as a precursor to further work.Comment: 9 pages, 6 figure
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