180 research outputs found
Expanding FLew with a Boolean connective
We expand FLew with a unary connective whose algebraic counterpart is the
operation that gives the greatest complemented element below a given argument.
We prove that the expanded logic is conservative and has the Finite Model
Property. We also prove that the corresponding expansion of the class of
residuated lattices is an equational class.Comment: 15 pages, 4 figures in Soft Computing, published online 23 July 201
A note on drastic product logic
The drastic product is known to be the smallest -norm, since whenever . This -norm is not left-continuous, and hence it
does not admit a residuum. So, there are no drastic product -norm based
many-valued logics, in the sense of [EG01]. However, if we renounce standard
completeness, we can study the logic whose semantics is provided by those MTL
chains whose monoidal operation is the drastic product. This logic is called
in [NOG06]. In this note we justify the study of this
logic, which we rechristen DP (for drastic product), by means of some
interesting properties relating DP and its algebraic semantics to a weakened
law of excluded middle, to the projection operator and to
discriminator varieties. We shall show that the category of finite DP-algebras
is dually equivalent to a category whose objects are multisets of finite
chains. This duality allows us to classify all axiomatic extensions of DP, and
to compute the free finitely generated DP-algebras.Comment: 11 pages, 3 figure
A temporal semantics for Nilpotent Minimum logic
In [Ban97] a connection among rough sets (in particular, pre-rough algebras)
and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we
present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95,
EG01]), in which the logic of every instant is given by {\L}3: a completeness
theorem will be shown. This is the prosecution of the work initiated in [AGM08]
and [ABM09], in which the authors construct a temporal semantics for the
many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table
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