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Multivalued logics and Topics
"... There are several practical problems of knowledge representation where it is more natural to talk in terms of the set of sentences related to a given topic than to make explicit all the sentences in this set. A problematic feature of classical logic is that if we want to represent this set by ..."
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by a small set which is closed under logical consequence, we can generate sentences related to new topics. For example from p it is possible to infer p q, even if q has no common topic with p. In this paper we compare several multivalued logics in order to give a formal characterisation
Multivalued logics and fuzzy reasoning
 BCS AISB Summer School
, 1975
"... These notes are concerned with recent developments in multivalued logic, particularly in fuzzy logic and its status as a model for human linguistic reasoning. This first section discusses the status of formal logic and the need for logics of approximate reasoning with vague data. The following secti ..."
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These notes are concerned with recent developments in multivalued logic, particularly in fuzzy logic and its status as a model for human linguistic reasoning. This first section discusses the status of formal logic and the need for logics of approximate reasoning with vague data. The following
On the Complexity of Entailment in Propositional Multivalued Logics
, 1997
"... Multivalued logics have a long tradition in the philosophy and logic literature that originates from the work by / Lukaszewicz in the 20's. More recently, many AI researchers have been interested in this topic for both semantic and computational reasons. Multivalued logics have indeed been freq ..."
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Multivalued logics have a long tradition in the philosophy and logic literature that originates from the work by / Lukaszewicz in the 20's. More recently, many AI researchers have been interested in this topic for both semantic and computational reasons. Multivalued logics have indeed been
Multivalued logic gates for quantum computation
 Phys. Rev. A
, 2000
"... We develop a multivalued logic for quantum computing for use in multilevel quantum systems, and discuss the practical advantages of this approach for scaling up a quantum computer. Generalizing the methods of binary quantum logic, we establish that arbitrary unitary operations on any number of dl ..."
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We develop a multivalued logic for quantum computing for use in multilevel quantum systems, and discuss the practical advantages of this approach for scaling up a quantum computer. Generalizing the methods of binary quantum logic, we establish that arbitrary unitary operations on any number of d
Stipulations, multivalued logic, and
"... Dedicated to Professor Ivo Rosenberg on the occasion of his sixtyfifth birthday A stipulation s is a map from a set Pr of propositional constants into the sentence algebra generated by that set. Given an algebra A of truth values a valuation f: Pr → A is sconsistent if f(p) = f̄(s(p)), for all p ..."
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Dedicated to Professor Ivo Rosenberg on the occasion of his sixtyfifth birthday A stipulation s is a map from a set Pr of propositional constants into the sentence algebra generated by that set. Given an algebra A of truth values a valuation f: Pr → A is sconsistent if f(p) = f̄(s(p)), for all p ∈ Pr, where f ̄ is the natural extension of f to the sentence algebra. If there is a partial order (an “information order”) ≤ on the domain of the algebra that is preserved by its fundamental operations, then the set of sconsistent valuations into the algebra is also a (nonempty) poset. Natural completeness properties of the partial order transfer to this poset (Theorem 3.7), and if the algebra is in addition ordercomplete with respect to the partial order the finite posets of sconsistent valuations can be characterized (Theorem 3.8). The results are applied and refined in the case A is the threeelement Kleene algebra (Section 4) and the fourelement De Morgan algebra (Section 5). The facts about the clones of operations needed for this are known in the Kleene case, and are provided for the De Morgan case: the fourelement De Morgan algebra with all four constants added to its type is ordercomplete with respect to a lattice order (Theorem 5.2), while the clone of operations of the fourelement De Morgan algebra consists of all selfdual maps preserving the same lattice order (Theorem 5.8). 1 1
A Multivalued Logic Approach to Integrating Planning and Control
 Artificial Intelligence
, 1995
"... Intelligent agents embedded in a dynamic, uncertain environment should incorporate capabilities for both planned and reactive behavior. Many current solutions to this dual need focus on one aspect, and treat the other one as secondary. We propose an approach for integrating planning and control base ..."
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to produce conjoint goals and complex controls. The ability of multivalued logics to represent graded preferences allows us to formulate tradeoffs in the combination. Two composition theorems relate complex controls to complex goals, and provide the key to using standard knowledgebased deliberation
Multivalued Logic Mapping of Neurons in Feedforward Networks
"... A common view of feedforward neural networks is that of a black box since the knowledge embedded in the connection weights of a feedforward neural network is generally considered incomprehensible. Many researchers have addressed this deficiency of neural networks by suggesting schemes to obtain a Bo ..."
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Boolean logic representation for the output of a neuron based on its connection weights. However, these schemes mostly assume binary inputs to the neural network. Since it is not uncommon to find multivalued discrete inputs to neurons, we present in this paper a weight mapping scheme that is capable
Model Checking for Multivalued Logic of Knowledge and Time
"... We present a multivalued µKcalculus, an expressive logic to specify knowledge and time in multiagent systems. We show that the general method of translation [22] from multivalued to twovalued De Morgan algebras can be extended to mv µKcalculus model checking. This way can we reduce the model che ..."
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We present a multivalued µKcalculus, an expressive logic to specify knowledge and time in multiagent systems. We show that the general method of translation [22] from multivalued to twovalued De Morgan algebras can be extended to mv µKcalculus model checking. This way can we reduce the model
Multivalued Logic to Transform Potential into Actual Objects
, 2007
"... Abstract. We define the notion of “potential existence ” by starting from the fact that in multivalued logic the existential quantifier is interpreted by the least upper bound operator. Besides, we try to define in a general way how to pass from potential into actual existence. ..."
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Abstract. We define the notion of “potential existence ” by starting from the fact that in multivalued logic the existential quantifier is interpreted by the least upper bound operator. Besides, we try to define in a general way how to pass from potential into actual existence.
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