Fixed-point logics on trees (original) (raw)

UvA-DARE ( Digital Academic Repository ) Fixed-point logics on trees

2010

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Intensional reasoning about knowledge

1987

As demands and ambitions increase in Artificial Intelligence, the need for formal systems that facilitate a study and a simulation of a machine cognition has become an inevitability. This paper explores and developes the foundations of a formal system for propositional reasoning about knowledge. The semantics of every meaningful expression in the system is fully determined by its intension, the set of complexes in which the expression is confirmed. The knowledge system is based on three zeroth-order theories of epistemic reasoning for consciousness, knowledge and entailed knowledge. The results presented in the paper determine the soundness and the completeness of the knowledge system. The modes of reasoning and the relations among the various epistemic notions emphasize the expressive power of the intensional paradigm. Ill ACKNOWLEDGEMENT To Dr. Arlan R. DeKock sui generis. He has been a mainstay of encouragement and advice throughout the years I spent at UMR. The intension and the influence of his Socratic mentorship will be reflected in the years to come. I want to express my gratitude to Dr. Gillett and his family for the gracious support given to me and my family. It has been a privilege to be a student of Dr. Gillett. My debts to Dr. Stanojevic for all the EE reasons that are beyond explanation. Dr. Metzner bestowed upon me, in his lectures, one of the most integral views on Computer Science. Moreover, he taught me that the road to understanding the bounded minimization takes detour via DO-loops. Sincere thanks to Dr. Ho for his kindness and genuine interest in the tradition, culture and history of the country I come from. My lasting appreciation and respect to the Fulbright Program for awarding me the honor of being a Fulbright Fellow and to the organizations that made it possible IIE, USIA, and the Binational Commission. An enduring gratitude to the University of Missouri-Rolla, extraordinary the Computer Science Department, which in the spirit of Fulbright accepted the fellowship and continued with the financial support without which it would have been impossible to continue with my studies. IV Finally, I would like to express my debt to my parents for the past and the present, to my wife for the present and the future, and to my children for the indefiniteness.

Life and Logic Reviewed by Hourya Benis Sinaceur

2007

Alfred Tarski (1901–1983) is one of the two greatest logicians of the twentieth century, the other being Kurt Gödel (1906–1978). Each began his career in Europe, respectively in Warsaw and Vienna, and came to America shortly before the Second World War. In contrast to the otherworldly Gödel, Tarski was ambitious and practical. He strove for, and succeeded at, building a school of logic at the University of California, Berkeley, that attracted students and distinguished researchers from all over the world. Tarski was the leader of the " semantic turn " in mathematical logic. This means that he achieved a shift from a view focused on formal systems, axioms, and rules of deduction to a view focusing on the relations between formal systems and their possible interpretations by usual mathematical theories such as real numbers or Cartesian geometry. Hence he gave precise definitions of semantic concepts that had been used informally before. The most important of those concepts a...