“Bulletin Board”

 School of Mathematics - June 14, 2004

Dissertation Defense

M. 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).

 
 
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).

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.


Information
Time:Monday, June 28, 2004, 10:00.
Place:School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran.


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