Z. Stachniak - Böcker

This text presents a new algebraic framework for the design and analysis of resolution-based automated reasoning systems for a range of non-classical logics. It develops an algebraic theory of resolution proof systems focusing on the problems of proof theory, representation and efficiency of the deductive process. A new class of logical calculi, the class of resolution logics, emerges as a second theme of the book. The logical and computational aspects of the relationship between resolution logics and resolution proof systems is explored in the context of monotonic as well as nonmonotonic reasoning. This book is aimed primarily at researchers and graduate students in artificial intelligence, symbolic and computational logic. The material is suitable as a reference book for researchers and as a text book for graduate courses on the theoretical aspects of automated reasoning and computational logic.

In the period between the two World Wars, Stanislaw Lesniewski, a prominent Polish logician, created his system of the foundations of mathematics, a system comprising three deductive theories: protothetic, ontology, and mereology. Lesniewski initiated his research programme in the foundations of mathematics in 1914 with his studies on a general theory of sets (to be later renamed "mereology"). The construction of ontology in the period between 1919 and 1921 marked the next step in the formation of Lesniewski's system. In order to combine mereology and ontology into a logically rigorous system, he constructed protothetic - the system of "first principles". Lesniewski's system of the foundations of mathematics was the "most thorough, original, and philosophically significant attempt to provide a logically secure foundation for the whole of mathematics" (Z. Jordan). This volume is a collection of the major contributions to protothetic, and includes the protothetic bibliography.

Stanislaw Lesniewski (1886-1939) was one of the leading Polish logicians and founders of the Warsaw School of Logic whose membership included, beside himself, Jan Lukasiewicz, Tadeusz Kotarbinski, Alfred Tarski, and many others. In his lifetime LeSniewski published only a few hundred pages. He produced many important results in many areas of mathematics; these stood in various relations to each other, and to materials produced by others, and, in time, created more and more editorial problems. Very many were left unpublished at the time of his death. Then in 1944 in the fire of Warsaw the whole of this material was burned and lost -a considerable loss since a great deal of what is important could have been reconstructed from these notes. The present publication aims at presenting unique Lesniewski's materials from alternative sources comprising lecture notes taken during some of Lesniewski's lectures and seminars delivered at the University of Warsaw be­ tween the two world wars. The editors are aware of the limitations of student notes which cannot compensate for the loss of the original materials. However, they are unique in reflecting Lesniewski's ideas as he himself presented them. Already at the time of his death it was realized that these notes would provide a unique access to Lesniewski's own thought as well as a valuable record of some of the activities of the Warsaw School of Logic.

Between the two world wars, Stanislaw Lesniewski (1886-1939), created the famous and important system of foundations of mathematics that comprises three deductive theories: Protothetic, Ontology, and Mereology. His research started in 1914 with studies on the general theory of sets (later named `Mereology'). Ontology followed between 1919 and 1921, and was the next step towards an integrated system. In order to combine these two systematically he constructed Protothetic - the system of `first principles'. Together they amount to what Z. Jordan called `... most thorough, original, and philosophically significant attempt to provide a logically secure foundation for the whole of mathematics'. The volume collects many of the most significant commentaries on, and contributions to, Protothetic. A Protothetic Bibliography is included.

Resolution Proof Systems: An Algebraic Theory presents a new algebraic framework for the design and analysis of resolution- based automated reasoning systems for a range of non-classical logics. It develops an algebraic theory of resolution proof systems focusing on the problems of proof theory, representation and efficiency of the deductive process. A new class of logical calculi, the class of resolution logics, emerges as a second theme of the book. The logical and computational aspects of the relationship between resolution logics and resolution proof systems is explored in the context of monotonic as well as nonmonotonic reasoning. This book is aimed primarily at researchers and graduate students in artificial intelligence, symbolic and computational logic. The material is suitable as a reference book for researchers and as a text book for graduate courses on the theoretical aspects of automated reasoning and computational logic.