Jon Barwise

A natural history of negation

This book offers a unique synthesis of past and current work on the structure, meaning, and use of negation and negative expressions, a topic that has engaged thinkers from Aristotle and the Buddha to Freud and Chomsky. Horns masterful study melds a review of scholarship in philosophy, psychology, and linguistics with original research, providing a full picture of negation in natural language and thought; this new edition adds a comprehensive preface and bibliography, surveying research since the books original publication.

Situation Theory and its Applications

Preface Part I. Situation Theory: 1. Constraints, channels, and the flow of information Jon Barwise 2. Extended Kamp notation: a graphical notation for situation theory Jon Barwise and Robin Cooper 3. States of affairs without parameters Mark Crimmins Part II. Logical Applications: 4. Labelled deductive systems and situation theory D. M. Gabbay 5. Events and processes in situation semantics Michael Georgeff, David Morley and Anand Rao 6. Nonmonotonic projection, causation and induction Robert C. Koons 7. Modal situation theory Stephen M. Schulz Part III. Linguistic Applications: 8. Generalized quantifiers and resource situations Robin Cooper 9. Situation theory and cooperative action Keith Devlin and Duska Rosenberg 10. Propositional and non-propositional attitudes Jonathan Ginzburg 11. Episodic logic: a situational logic for natural language processing Chung Hee Hwang and Lenhart K. Schubert 12. A situation-theoric formalization of definite description interpretation in plan elaboration dialogues Massimo Poessio 13. A situation-theoretic representation of text meaning anaphora, quantification, and negation Dag Westerstahl, Bjorn Haglund and Torbjorn Lager Name index Subject index.

On branching quantifiers in English

One of Hintikkas aims, in the paper Hintikka (1974),3 was to show that there are simple sentences of English which contain essential uses of branching quantification. If he is correct, it is a discovery with significant implications for linguistics, for the philosophy of natural language, and perhaps even for mathematical logic. Philosophically, it would influence our views of the ontological commitment inherent in specific natural language constructions, since branching quantification is a way of hiding quantification over various kinds of abstract abstract objects (functions from individuals to individuals, sets of individuals, etc.). Linguistically, the discovery of branching quantification would force us to re-examine, and perhaps re-interpret, Freges principle of compositionality according to which the meaning of a given expression is determined by the meanings of its constituent phrases. For example, the meaning of a branching quantifier expression of logic like:

An Introduction to First-Order Logic

Publisher Summary This chapter discusses the formulas that are certain finite strings of symbols. The “first” in the phrase “first-order logic” is to distinguish this form of logic from stronger logics, such as second-order or weak second-order logic, where certain extralogical notions (set or natural number) are taken as given in advance. The chapter provides information of what can and what cannot be expressed in first-order logic. Most of the examples are taken from the wealth of notions in modern algebra with which most mathematicians have at least a nodding acquaintance. The chapter also discusses many-sorted first-order logic, ω-logic, weak second-order logic, Infinitary logic, Logic with new quantifiers, and abstract model theory.

Three views of common knowledge

This paper investigates the relationships between three different views of common knowledge: the iterate approach, the fixed point approach, and the shared environment approach. We show that no two of these approaches are equivalent, contrary to accepted wisdom. We argue that the fixed point is the best conceptual analysis of the pretheoretic notion, but that the shared environment approach has its own role to play in understanding how common knowledge is used. We also discuss the assumptions under which various versions of the iterate approach are equivalent to the fixed point approach. We find that, for common knowledge, these assumptions are false, but that for simply having information, the assumptions are not so implausible, at least in the case of finite situations.

An Introduction to Recursively Saturated and Resplendent Models

The notions of recursively saturated and resplendent models grew out of the study of admissible sets with urelements and admissible fragments of L ω1ω , but, when applied to ordinary first order model theory, give us new tools for research and exposition. We will discuss their history in §3. The notion of saturated model has proven to be important in model theory. Its most important property for applications is that if , are saturated and of the same cardinality then = iff ≅ . See, e.g., Chang-Keisler [3]. The main drawback is that saturated models exist only under unusual assumptions of set theory. For example, if 2 κ = κ + then every theory T of L has a saturated model of power κ + . (Similarly, if κ is strongly inaccessible, then every T has a saturated model of power κ.) On the other hand, a theory T like Peano arithmetic, with types, cannot have a saturated model in any power κ with ω ≤ κ ≤ . One method for circumventing these problems of existence (or rather non-existence) is the use of “special” models (cf. [3]). If κ = Σ λ 2 λ , κ T of L has a special model of power κ. Such cardinals are large and, themselves, rather special. There are definite aesthetic objections to the use of these large, singular models to prove results about first order logic.

Interpolation, Preservation, and Pebble Games

Preservation and interpolation results are obtained for L1! and sublog-ics L L1! such that equivalence in L can be characterized by suitable back-and-forth conditions on sets of partial isomorphisms.

Some applications of Henkin quantifiers

We show how to approximate a Henkin formula by first order formulas. This method of approximation is then applied to problems of axiomatizing classes of structures.

Hanf numbers for fragments of ℶ h (A)

We describe an ordinalh(A) which plays a key role in the model theory of the admissible fragmentLA. In particular, the Hanf number ofLA is ℶh(A) IfLA isLκ=ω wherecf(k)>ω thenh(A) can be characterized as the least ordinal which is notH(k+)-recursive.

Applications of Strict Pi 1 1 Predicates to Infinitary Logic.

Consider the predicate of natural numbers defined by: where R is recursive. If, as usual, the variable ƒ ranges over ω ω (the set of functions from natural numbers to natural numbers) then this is just the usual normal form for Π 1 1 sets. If, however, ƒ ranges over 2 ω (the set of functions from ω into {0, 1}) then every such predicate is recursively enumerable. 3 Thus the second type of formula is generally ignored. However, the reduction just mentioned requires proof, and the proof uses some form of the Brower-Konig Infinity Lemma.