Existential rigidity and many modalities in order-sorted logic |
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Authors: | Ken Kaneiwa |
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Affiliation: | 1. UECE - State University of Ceará, Brazil;2. IFES - Federal Institute of Technology of Espírito Santo State, Brazil;3. Associated researcher at the State University of Ceará - UECE;4. Associated professor at the Federal Institute of Technology of Espírito Santo State - IFES;5. Titular professor at the State University of Ceará - UECE;1. Graduate Program in Computer Science, PPGI, UFES - Federal University of Espírito Santo, Av. Fernando Ferrari 514, Vitória CEP: 29060-270, Brazil;2. Production Engineering Department, UFES - Federal University of Espírito Santo, Av. Fernando Ferrari 514, Vitória CEP: 29060-270, Brazil |
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Abstract: | Order-sorted logic is a useful tool for knowledge representation and reasoning because it enables representation of sorted terms and formulas along with partially ordered sorts (called sort-hierarchy). However, this logic cannot represent more complex sorted expressions when they are true in any possible world (as rigid) or some possible worlds (as modality) such as time, space, belief, or situation. In this study, we extend order-sorted logic by introducing existential rigidity and many modalities. In the extended logic, sorted modal formulas are interpreted over the Cartesian product of sets of possible worlds. We present a new labeled tableau calculus to check the (un)satisfiability and validity of sorted modal formulas. |
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