We prove completeness, interpolation, decidability and an omitting types theorem for certain multi-dimensional modal logics where the states are not abstract entities but have an inner structure. The states will be sequences. Our approach is algebraic addressing varieties generated by complex algebras of Kripke semantics for such logics. The algebras dealt with are common cylindrification free reducts of cylindric and polyadic algebras. For finite dimensions, we show that such varieties are finitely axiomatizable, have the super amalgamation property, and that the subclasses consisting of only completely representable algebras are elementary, and are also finitely axiomatizable in first order logic. Also their modal logics have an N P complete satisfiability problem. Analogous results are obtained for infinite dimensions by replacing finite axiomatizability by finite schema axiomatizability.
Ahmed, T. S., Completions, Complete representations and Omitting types, in , 186–205.
Ahmed, T. S., Completions, Complete representations and Omitting types, in , 186–205.)| false
Andréka, H., Németi, I. and Ahmed, T. S., A nonrepresentable infinite dimensional quasi-polyadic equality algebra with a representable cylindric reduct, Studia Scientiarum Mathematicarum Hungarica, 50 (1) (2013), pp. 116.
Andréka, H., Németi, I. and Ahmed, T. S., A nonrepresentable infinite dimensional quasi-polyadic equality algebra with a representable cylindric reduct, Studia Scientiarum Mathematicarum Hungarica, 50 (1) (2013), pp. 116.)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
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