On some Substructural Logics

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On some Substructural Logics

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dc.contributor.advisor Kapetanović, Miodrag
dc.contributor.author Isaković-Ilić, Mirjana en_US
dc.date.accessioned 2009-12-03T12:15:00Z
dc.date.available 2009-12-03T12:15:00Z
dc.identifier.uri http://hdl.handle.net/123456789/201
dc.description.abstract In this thesis cut elimination and decidability for several propositional substructural logics are studied. The thesis consists of nine chapters. Chapters 2-6 make the first part of the thesis. In that part sequent systems for substrictural logics are formulated. In Chapters 3 and 4 for each of these systems an algebraic structure is given and completeness and consistency are proved. In Chapters 5 and 6 cut elimination and decidability for these systems are studied. It is well known that sequent system of classical Lambek logic, the system SL is decidable and that cut is not an admissible rule in CL. Another sequent system for classical Lambek logic, the system CL* is formulated, and the elimination of cut in CL* is proved. The system CL* does not posses the subformula property, so decidability for classical Lambek logic is not the direct consequence of the cut-elimination procedure in CL*. However, on the basis of the cut elimination procedure in CL*, a procedure for deciding of whether a sequent is provable in CL* or not is given (i. e., a new (pure syntactic) proof of decidability for classical Lambek logic is given). The same result is shown for classical Lambek logic with weakening. In the second part of the thesis (chapters 7-9), by using that proof, an algorithm (based on the tableau method) is formulated for deciding whether or not a formula is the theorem in any of considered substructural logics. en
dc.description.provenance Made available in DSpace on 2009-12-03T12:15:00Z (GMT). No. of bitstreams: 1 phdMirjanaIsakovicIlic.pdf: 1047741 bytes, checksum: 2ec2148fd211beb34b11a1e20d401f6e (MD5) en
dc.publisher Belgrade en_US
dc.title On some Substructural Logics en_US
dc.title.alternative O nekim supstrukturnim logikama sr
mf.subject.keywords substructural logics, proof theory, cut elimination, decidability, tableaux
mf.contributor.committee Božić, Milan; Petrić, Zoran

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