Abstracts Vol. 10-No 1/ 2000

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Specification of nonmonotonic reasoning -Joeri Engelfriet, Jan Treur
Abstract: .
Keywords:

Process Algebra with Four-Valued Logic - Jan A. Bergstra, Alban Ponse
Abstract:. We propose a combination of a fragment of four-valued logic and process algebra. This fragment is geared to a simple relation with process algebra via the conditional guard construct, and can easily be extended to a truth-functionally complete logic. We present an operational semantics in SOS-style, and a completeness result for ACP with conditionals and four-valued logic. Completeness is preserved under the restriction to some other non-classical logics.
Keywords: Process Algebra, Many-Valued Logic, Conditional Guard Construct, Conditional Composition.

Evidence theory in multivalued models of modal logic - Elena Tsiporkova, Bernard De Baets, Veselka Boeva
Abstract:. A modal logic interpretation of Dempster--Shafer theory is developed in the framework of multivalued models of modal logic, i.e. models in which in any possible world an arbitrary number (possibly zero) of atomic propositions can be true. Several approaches to conditioning in multivalued models of modal logic are presented.
Keywords: Accessibility relation, Basic probability assignment, Belief measure, Commonality function, Modal logic, Multivalued mapping, Plausibility measure, Value assignment function.

Regular bilattices -Alexej P. Pynko
Abstract:. A bilattice is said to be regular provided its truth conjunction and disjunction are monotonic with respect to its knowledge ordering. The principal result of this paper is that the following properties of a bilattice B are equivalent:
B is regular;
the truth conjunction and disjunction of B are definable through the rest of the operations and constants of B;
B is isomorphic to a bilattice of the form L1 o L2 where L1 and L2 are bounded lattices.
We also derive from this metaequivalence a number of corollaries concerning distributive bilattices, degenerated bilattices and bilattices with negation.
Keywords: bounded lattice, pure bilattice, truth lattice, knowledge lattice, regular bilattice, degenerated bilattice, distributive bilattice, inversion, negation.

Structure of left-continuous triangular norms with strong induced negations - S\'{a}ndor Jenei
Abstract:. A new algebraic construction -called rotation- is introduced in this paper which from any left-continuous triangular norm which has no zero divisors produces a left-continuous but not continuous triangular norm with strong induced negation. An infinite number of new families of such triangular norms can be constructed in this way which provides a huge spectrum of choice for e.g. logical and set theoretical connectives in non-classical logic and in fuzzy theory. On the other hand, the introduced construction brings us closer to the understanding the structure of these connectives and the corresponding logics. From the application point of view, results of this paper can be especially useful in the field of non-classical logic, fuzzy sets, and fuzzy preference modeling.
Keywords: Conjunction, Triangular norm, Implication, Residual implication, Induced negation, Construction, Left-continuity, Rotation.

Journal of Applied Non-Classical Logics
Volume 10- No 1/ 1999


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