Dissertation DefenseM. Alizadeh, the fourth Ph.D. student of IPM in Mathematical Logic, is going to defend his thesis entitled "Algebraic Analysis of Basic Propositional Logic" on Monday, June 28, 2004. His supervisor is Prof. M. Ardeshir (Sharif University of Technology). |
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M. Alizadeh, the fourth Ph.D. student of IPM in Mathematical Logic, defended his thesis entitled "Algebraic Analysis of Basic Propositional Logic". His supervisor was Prof. M. Ardeshir (Sharif University of Technology).
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Abstract |
We study the algebraic semantics of Basic Propositional Calculus,
BPC, which was introduced by M. Ardeshir in 1995. The
algebraic structure associated with BPC is called Basic
algebra, Ba. We study the algebraic counterparts for
disjunction, interpolation and faithfulness properties in
BPC. Among other things, we prove that the class of all
Ba 's has the amalgamation property. The notion of
faithfulness is defined in algebraic terms and a completeness
theorem is proved for faithful theories with respect to the class
of all faithful Ba 's. It is shown that the class of all
faithful Ba 's has the amalgamation property and that is
equivalent to faithful theories having the interpolation property.
We also study algebraic semantics for some natural extensions of
BPC, e.g., Linear BPC and Formal propositional
calculus, FPC. We show that the class of all linear
faithful Basic algebras and finite irreflexive Formal algebras
have the amalgamation property.
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| Information |
| Time: | Monday, June 28, 2004, 10:00. |
| Place: | School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran. |
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