Abstract

AbstractWe introduce a new semantics for the (full) Lambek calculus, which is based on an automata-theoretic construction. This automata-theoretic semantics combines languages and relations via closure operators which are based on automaton transitions. We establish the strong completeness of this semantics for the full Lambek calculus via an isomorphism theorem for the syntactic concepts lattice of a language and a construction for the universal automaton recognizing the same language. Automata-theoretic semantics is interesting because it connects two important semantics of the Lambek calculus, namely the relational and the language-theoretic. At the same time, it establishes a strong relation between two canonical constructions over a given language, namely its syntactic concept lattice and its universal automaton.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.