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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.
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Very many were left unpublished at the time of his death.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."
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.
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.
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."
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