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This book aims to lay bare the logical foundations of tractable
reasoning. It draws on Marvin Minsky's seminal work on frames,
which has been highly influential in computer science and, to a
lesser extent, in cognitive science. Only very few people have
explored ideas about frames in logic, which is why the
investigation in this book breaks new ground. The apparent
intractability of dynamic, inferential reasoning is an unsolved
problem in both cognitive science and logic-oriented artificial
intelligence. By means of a logical investigation of frames and
frame concepts, Andreas devises a novel logic of tractable
reasoning, called frame logic. Moreover, he devises a novel belief
revision scheme, which is tractable for frame logic. These
tractability results shed new light on our logical and cognitive
means to carry out dynamic, inferential reasoning. Modularity
remains central for tractability, and so the author sets forth a
logical variant of the massive modularity hypothesis in cognitive
science. This book conducts a sustained and detailed examination of
the structure of tractable and intelligible reasoning in cognitive
science and artificial intelligence. Working from the perspective
of formal epistemology and cognitive science, Andreas uses
structuralist notions from Bourbaki and Sneed to provide new
foundational analyses of frames, object-oriented programming,
belief revision, and truth maintenance. Andreas then builds on
these analyses to construct a novel logic of tractable reasoning he
calls frame logic, together with a novel belief revision scheme
that is tractable for frame logic. Put together, these logical
analyses and tractability results provide new understandings of
dynamic and inferential reasoning. Jon Doyle, North Carolina State
University
This book aims to lay bare the logical foundations of tractable
reasoning. It draws on Marvin Minsky's seminal work on frames,
which has been highly influential in computer science and, to a
lesser extent, in cognitive science. Only very few people have
explored ideas about frames in logic, which is why the
investigation in this book breaks new ground. The apparent
intractability of dynamic, inferential reasoning is an unsolved
problem in both cognitive science and logic-oriented artificial
intelligence. By means of a logical investigation of frames and
frame concepts, Andreas devises a novel logic of tractable
reasoning, called frame logic. Moreover, he devises a novel belief
revision scheme, which is tractable for frame logic. These
tractability results shed new light on our logical and cognitive
means to carry out dynamic, inferential reasoning. Modularity
remains central for tractability, and so the author sets forth a
logical variant of the massive modularity hypothesis in cognitive
science. This book conducts a sustained and detailed examination of
the structure of tractable and intelligible reasoning in cognitive
science and artificial intelligence. Working from the perspective
of formal epistemology and cognitive science, Andreas uses
structuralist notions from Bourbaki and Sneed to provide new
foundational analyses of frames, object-oriented programming,
belief revision, and truth maintenance. Andreas then builds on
these analyses to construct a novel logic of tractable reasoning he
calls frame logic, together with a novel belief revision scheme
that is tractable for frame logic. Put together, these logical
analyses and tractability results provide new understandings of
dynamic and inferential reasoning. Jon Doyle, North Carolina State
University
This book covers work written by leading scholars from different
schools within the research area of paraconsistency. The authors
critically investigate how contemporary paraconsistent logics can
be used to better understand human reasoning in science and
mathematics. Offering a variety of perspectives, they shed a new
light on the question of whether paraconsistent logics can function
as the underlying logics of inconsistent but useful scientific and
mathematical theories. The great variety of paraconsistent logics
gives rise to various, interrelated questions, such as what are the
desiderata a paraconsistent logic should satisfy, is there prospect
of a universal approach to paraconsistent reasoning with axiomatic
theories, and to what extent is reasoning about sets structurally
analogous to reasoning about truth. Furthermore, the authors
consider paraconsistent logic's status as either a normative or
descriptive discipline (or one which falls in between) and which
inconsistent but non-trivial axiomatic theories are well understood
by which types of paraconsistent approaches. This volume addresses
such questions from different perspectives in order to (i) obtain a
representative overview of the state of the art in the
philosophical debate on paraconsistency, (ii) come up with fresh
ideas for the future of paraconsistency, and most importantly (iii)
provide paraconsistent logic with a stronger philosophical
foundation, taking into account the developments within the
different schools of paraconsistency.
This book covers work written by leading scholars from different
schools within the research area of paraconsistency. The authors
critically investigate how contemporary paraconsistent logics can
be used to better understand human reasoning in science and
mathematics. Offering a variety of perspectives, they shed a new
light on the question of whether paraconsistent logics can function
as the underlying logics of inconsistent but useful scientific and
mathematical theories. The great variety of paraconsistent logics
gives rise to various, interrelated questions, such as what are the
desiderata a paraconsistent logic should satisfy, is there prospect
of a universal approach to paraconsistent reasoning with axiomatic
theories, and to what extent is reasoning about sets structurally
analogous to reasoning about truth. Furthermore, the authors
consider paraconsistent logic's status as either a normative or
descriptive discipline (or one which falls in between) and which
inconsistent but non-trivial axiomatic theories are well understood
by which types of paraconsistent approaches. This volume addresses
such questions from different perspectives in order to (i) obtain a
representative overview of the state of the art in the
philosophical debate on paraconsistency, (ii) come up with fresh
ideas for the future of paraconsistency, and most importantly (iii)
provide paraconsistent logic with a stronger philosophical
foundation, taking into account the developments within the
different schools of paraconsistency.
The content in Chapter 1-3 is a fairly standard one-semester course
on local rings with the goal to reach the fact that a regular local
ring is a unique factorization domain. The homological machinery is
also supported by Cohen-Macaulay rings and depth. In Chapters 4-6
the methods of injective modules, Matlis duality and local
cohomology are discussed. Chapters 7-9 are not so standard and
introduce the reader to the generalizations of modules to complexes
of modules. Some of Professor Iversen's results are given in
Chapter 9. Chapter 10 is about Serre's intersection conjecture. The
graded case is fully exposed. The last chapter introduces the
reader to Fitting ideals and McRae invariants.
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