862 research outputs found
Complexity of fuzzy answer set programming under Ćukasiewicz semantics
Fuzzy answer set programming (FASP) is a generalization of answer set programming (ASP) in which propositions are allowed to be graded. Little is known about the computational complexity of FASP and almost no techniques are available to compute the answer sets of a FASP program. In this paper, we analyze the computational complexity of FASP under Ćukasiewicz semantics. In particular we show that the complexity of the main reasoning tasks is located at the first level of the polynomial hierarchy, even for disjunctive FASP programs for which reasoning is classically located at the second level. Moreover, we show a reduction from reasoning with such FASP programs to bilevel linear programming, thus opening the door to practical applications. For definite FASP programs we can show P-membership. Surprisingly, when allowing disjunctions to occur in the body of rules â a syntactic generalization which does not affect the expressivity of ASP in the classical case â the picture changes drastically. In particular, reasoning tasks are then located at the second level of the polynomial hierarchy, while for simple FASP programs, we can only show that the unique answer set can be found in pseudo-polynomial time. Moreover, the connection to an existing open problem about integer equations suggests that the problem of fully characterizing the complexity of FASP in this more general setting is not likely to have an easy solution
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
Pavelka-style completeness in expansions of \L ukasiewicz logic
An algebraic setting for the validity of Pavelka style completeness for some
natural expansions of \L ukasiewicz logic by new connectives and rational
constants is given. This algebraic approach is based on the fact that the
standard MV-algebra on the real segment is an injective MV-algebra. In
particular the logics associated with MV-algebras with product and with
divisible MV-algebras are considered
The problem of artificial precision in theories of vagueness: a note on the role of maximal consistency
The problem of artificial precision is a major objection to any theory of
vagueness based on real numbers as degrees of truth. Suppose you are willing to
admit that, under sufficiently specified circumstances, a predication of "is
red" receives a unique, exact number from the real unit interval [0,1]. You
should then be committed to explain what is it that determines that value,
settling for instance that my coat is red to degree 0.322 rather than 0.321. In
this note I revisit the problem in the important case of {\L}ukasiewicz
infinite-valued propositional logic that brings to the foreground the role of
maximally consistent theories. I argue that the problem of artificial
precision, as commonly conceived of in the literature, actually conflates two
distinct problems of a very different nature.Comment: 11 pages, 2 table
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