This volume tackles the slippery subject of 'meaning'.

This book brings together several directions of work in model theory between the late 1950s and early 1980s.

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. (shrink)

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.

Presents a mathematically rigorous, philosophically sound foundation for a science of information.

One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers explore (...) the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information. (shrink)

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. (shrink)

Covers first-order language in method appropriate for first and second courses in logic. CD-ROM consists of a new book, 3 programs,and an Internet-based grading service.

In recent years much effort has gone into the study of languages which strengthen the classical first-order predicate calculus in various ways. This effort has been motivated by the desire to find a language which is(I) strong enough to express interesting properties not expressible by the classical language, but(II) still simple enough to yield interesting general results. Languages investigated include second-order logic, weak second-order logic, ω-logic, languages with generalized quantifiers, and infinitary logic.

In this paper I explore informationalism, a pragmatic theory of modality that seems to solve some serious problems in the familiar possible worlds accounts of modality. I view the theory as an elaboration of Stalnaker's moderate modal realism, though it also derives from Dretske's semantic theory of information. Informationalism is presented in Section 2 after the prerequisite stage setting in Section 1. Some applications are sketched in Section 3. Finally, a mathematical model of the theory is developed in Section 4.How (...) many times have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth? (Arthur Conan Doyle)You've put me in an impossible situation. (Anonymous)[N]othing we imagine is absolutely impossible. (David Hume). (shrink)

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. (shrink)

Preface This volume represents the proceedings of the Second Conference on Situation Theory and its Applications, held at Loch Rannoch, Scotland, ...

Preservation and interpolation results are obtained for L ∞ω and sublogics $\mathscr{L} \subseteq L_{\infty\omega}$ such that equivalence in L can be characterized by suitable back-and-forth conditions on sets of partial isomorphisms.

We show that several theorems on ordinal bounds in different parts of logic are simple consequences of a basic result in the theory of global inductive definitions.

This paper is an investigation into the logic of information flow. The basic perspective is that logic flows in virtue of constraints and that constraints classify channels connecting particulars In this paper we explore some logics intended to model reasoning in the case of idealized information flow, that is, where the constraints involved are exceptionless. We look at this as a step toward the far more challenging task of understanding the logic of imperfect information flow, that is where the constraints (...) admit of exceptional connections. This paper continues and amplifies work presented by the same authors in [10]. (shrink)

This paper considers the correspondence theory from modal logic and obtains correspondence results for models as opposed to frames. The key ideas are to consider infinitary modal logic, to phrase correspondence results in terms of substitution instances of a given modal formula, and to identify bisimilar model-world pairs.

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.