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This textbook/software package covers first-order language in a
method appropriate for a wide range of courses, from first logic
courses for undergraduates (philosophy, mathematics, and computer
science) to a first graduate logic course. The accompanying online
grading service instantly grades solutions to hundreds of computer
exercises. The second edition of "Language, Proof and Logic"
represents a major expansion and revision of the original package
and includes applications for mobile devices, additional exercises,
a dedicated website, and increased software compatibility and
support.
Circular analyses of philosophical, linguistic, or computational
phenomena have been attacked on the assumption that they conflict
with mathematical rigour. Barwise and Moss have undertaken to prove
this assumption false. This volume is concerned with extending the
modelling capabilities of set theory to provide a uniform treatment
of circular phenomena. As a means of guiding the reader through the
concrete examples of the theory, the authors have included many
exercises and solutions: these exercises range in difficulty and
ultimately stimulate the reader to come up with new results.
Vicious Circles is intended for use by researchers who want to use
hypersets; although some experience in mathematics is necessary,
the book is accessible to people with widely differing backgrounds
and interests.
"Tarski's World" is an innovative and exciting method of
introducing students to the language of first-order logic. Using
the courseware package, students quickly master the meanings of
connectives and qualifiers and soon become fluent in the symbolic
language at the core of modern logic. The program allows students
to build three-dimensional worlds and then describe them in
first-order logic. The program, compatible with Macintosh and PC
formats, also contains a unique and effective corrective tool in
the form of a game, which methodically leads students back through
their errors if they wrongly evaluate the sentences in the
constructed worlds.
A brand new feature in this revised and expanded edition is student
access to Grade Grinder, an innovative Internet-based grading
service that provides accurate and timely feedback to students
whenever they need it. Students can submit solutions for the
program's more than 100 exercises to the Grade Grinder for
assessment, and the results are returned quickly to the students
and optionally to the teacher as well. A web-based interface also
allows instructors to manage assignments and grades for their
classes.
Intended as a supplement to a standard logic text, "Tarski's World"
is an essential tool for helping students learn the language of
logic.
Since their inception, the Perspectives in Logic and Lecture Notes
in Logic series have published seminal works by leading logicians.
Many of the original books in the series have been unavailable for
years, but they are now in print once again. Admissible set theory
is a major source of interaction between model theory, recursion
theory and set theory, and plays an important role in definability
theory. In this volume, the seventh publication in the Perspectives
in Logic series, Jon Barwise presents the basic facts about
admissible sets and admissible ordinals in a way that makes them
accessible to logic students and specialists alike. It fills the
artificial gap between model theory and recursion theory and covers
everything the logician should know about admissible sets.
Information is a central topic in computer science, cognitive science, and philosophy. In spite of its importance in the "information age," there is no consensus on what information is, what makes it possible, and what it means for one medium to carry information about another. Drawing on ideas from mathematics, computer science, and philosophy, this book addresses the definition and place of information in society. The authors, observing that information flow is possible only within a connected distribution system, provide a mathematically rigorous, philosophically sound foundation for a science of information. They illustrate their theory by applying it to a wide range of phenomena, from file transfer to DNA, from quantum mechanics to speech act theory.
This research text addresses the logical aspects of the visualization of information with papers especially commissioned for this book. The authors explore the logical properties of diagrams, charts, maps, and the like, and their use in problem solving and in teaching basic reasoning skills. As computers make visual presentations of information even more commonplace,it becomes increasingly important for the research community to develop an understanding of such tools.
In this provocative book, Barwise and Perry tackle the slippery
subject of 'meaning', a subject that has long vexed linguists,
language philosophers, and logicians. Meaning does not exist solely
within words and sentences but resides largely in the situation and
the attitudes brought to it by those involved. The authors present
an unusually lucid treatment of important innovations in the field
of natural semantics, contending that the standard view of logic
(as derived from Frege, Russell, and work in mathematics and logic)
is inappropriate for many of the uses to which it has been put by
scholars. In Situations and Attitudes Barwise and Perry provide the
basics of a realistic model-theoretic semantics of natural
language, explain the main ideas of the theory, and contrast them
with those of competing theories.
The Logical Reasoning with Diagrams and Sentences courseware
package teaches the principles of analytical reasoning and proof
construction using a carefully crafted combination of textbook,
desktop, and online materials. This package is sure to be an
essential resource in a range of courses incorporating logical
reasoning, including formal linguistics, philosophy, mathematics,
and computer science. Unlike traditional formal treatments of
reasoning, this package uses both graphical and sentential
representations to reflect common situations in everyday reasoning
where information is expressed in many forms, such as finding your
way to a location using a map and an address. It also teaches
students how to construct and check the logical validity of a
variety of proofs of consequence and non-consequence, consistency
and inconsistency, and independence using an intuitive proof system
which extends standard proof treatments with sentential, graphical,
and heterogeneous inference rules, allowing students to focus on
proof content rather than syntactic structure. Building upon the
widely used Tarski's World and Language, Proof and Logic courseware
packages, Logical Reasoning with Diagrams and Sentences contains
more than three hundred exercises, most of which can be assessed by
the Grade Grinder online assessment service; is supported by an
extensive website through which students and instructors can access
online video lectures by the authors; and allows instructors to
create their own exercises and assess their students' work.Logical
Reasoning with Diagrams and Sentences is an expanded revision of
the Hyperproof courseware package.
Information is a central topic in computer science, cognitive
science, and philosophy. In spite of its importance in the
"information age," there is no consensus on what information is,
what makes it possible, and what it means for one medium to carry
information about another. Drawing on ideas from mathematics,
computer science, and philosophy, this book addresses the
definition and place of information in society. The authors,
observing that information flow is possible only within a connected
distribution system, provide a mathematically rigorous,
philosophically sound foundation for a science of information. They
illustrate their theory by applying it to a wide range of
phenomena, from file transfer to DNA, from quantum mechanics to
speech act theory.
Bringing together powerful new tools from set theory and the
philosophy of language, this book proposes a solution to one of the
few unresolved paradoxes from antiquity, the Paradox of the Liar.
Treating truth as a property of propositions, not sentences, the
authors model two distinct conceptions of propositions: one based
on the standard notion used by Bertrand Russell, among others, and
the other based on J.L. Austin's work on truth. Comparing these two
accounts, the authors show that while the Russellian conception of
the relation between sentences, propositions, and truth is
crucially flawed in limiting cases, the Austinian perspective has
fruitful applications to the analysis of semantic paradox. In the
course of their study of a language admitting circular reference
and containing its own truth predicate, Barwise and Etchemendy also
develop a wide range of model-theoretic techniques--based on a new
set-theoretic tool, Peter Aczel's theory of hypersets--that open up
new avenues in logical and formal semantics.
Situation Theory and situation semantics are recent approaches to
language and information, approaches first formulated by Jon
Barwise and John Perry in Situations and Attitudes (1983). The
present volume collects some of Barwise's papers written since
then, those directly concerned with relations among logic,
situation theory, and situation semantics. Several papers appear
here for the first time.
Situation theory is the result of an interdisciplinary effort to
create a full-fledged theory of information. Created by scholars
and scientists from cognitive science, computer science, AI,
linguistics, logic, philosophy, and mathematics, the theory is
forging a common set of tools for the analysis of phenomena from
all these fields. This volume presents work that evolved out of the
Second Conference on Situation Theory and its Applications.
Twenty-six essays exhibit the wide range of the theory, covering
such topics as natural language semantics, philosophical issues
about information, mathematical applications, and the visual
representation of information in computer systems.Jon Barwise is a
professor of philosophy, mathematics, and logic at Indiana
University in Bloomington. Jean Mark Gawron is a researcher at SRI
International and a consultant at Hewlett-Packard Laboratories.
Gordon Plotkin is a professor of theoretical computer science at
the University of Edinburgh. Syun Tutiya is in the philosophy
department at Chiba University in Japan.
Hyperproof is a system for learning the principles of analytical
reasoning and proof construction, consisting of a text and a
Macintosh software program. Unlike traditional treatments of
first-order logic, Hyperproof combines graphical and sentential
information, presenting a set of logical rules for integrating
these different forms of information. This strategy allows students
to focus on the information content of proofs, rather than the
syntactic structure of sentences. Using Hyperproof the student
learns to construct proofs of both consequence and nonconsequence
using an intuitive proof system that extends the standard set of
sentential rules to incorporate information represented
graphically. Hyperproof is compatible with various
natural-deduction-style proof systems, including the system used in
the authors' Language of First-Order Logic.
Situation theory is the result of an interdisciplinary effort to
create a full-fledged theory of information. Created by scholars
and scientists from cognitive science, computer science, AI,
linguistics, logic, philosophy, and mathematics, the theory is
forging a common set of tools for the analysis of phenomena from
all these fields. This volume presents work that evolved out of the
Second Conference on Situation Theory and its Applications.
Twenty-six essays exhibit the wide range of the theory, covering
such topics as natural language semantics, philosophical issues
about information, mathematical applications, and the visual
representation of information in computer systems.Jon Barwise is a
professor of philosophy, mathematics, and logic at Indiana
University in Bloomington. Jean Mark Gawron is a researcher at SRI
International and a consultant at Hewlett-Packard Laboratories.
Gordon Plotkin is a professor of theoretical computer science at
the University of Edinburgh. Syun Tutiya is in the philosophy
department at Chiba University in Japan.
The Language of First-Order Logic is a complete introduction to
first-order symbolic logic, consisting of a computer program and a
text. The program, an aid to learning and using symbolic notation,
allows one to construct symbolic sentences and possible worlds, and
verify that a sentence is well formed. The truth or falsity of a
sentence can be determined by playing a deductive game with the
computer.
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