1. 1 OBJECTIVES The main objective of this joint work is to bring together some ideas that have played central roles in two disparate theoretical traditions in order to con tribute to a better understanding of the relationship between focus and the syn tactic and semantic structure of sentences. Within the Prague School tradition and the branch of its contemporary development represented by Hajicova and Sgall (HS in the sequel), topic-focus articulation has long been a central object of study, and it has long been a tenet of Prague school linguistics that topic-focus structure has systematic relevance to meaning. Within the formal semantics tradition represented by Partee (BHP in the sequel), focus has much more recently become an area of concerted investigation, but a number of the semantic phenomena to which focus is relevant have been extensively investi gated and given explicit compositional semantic-analyses. The emergence of 'tripartite structures' (see Chapter 2) in formal semantics and the partial simi larities that can be readily observed between some aspects of tripartite structures and some aspects of Praguian topic-focus articulation have led us to expect that a closer investigation of the similarities and differences in these different theoretical constructs would be a rewarding undertaking with mutual benefits for the further development of our respective theories and potential benefit for the study of semantic effects of focus in other theories as well."

This collection of papers stems originally from a conference on Property Theory, Type Theory and Semantics held in Amherst on March 13-16 1986. The conference brought together logicians, philosophers, com puter scientists and linguists who had been working on these issues (of ten in isolation from one another). Our intent was to boost debate and exchange of ideas on these fundamental issues at a time of rapid change in semantics and cognitive science. The papers published in this work have evolved substantially since their original presentation at the conference. Given their scope, we thought it convenient to divide the work into two volumes. The first deals primarily with logical and philosophical foundations, the second with more empirical semantic issues. While there is a common set of issues tying the two volumes together, they are both self-contained and can be read independently of one another. Two of the papers in the present collection (van Benthem in volume 1 and Chierchia in volume II) were not actually read at the conference. They are nevertheless included here for their direct relevance to the topics of the volumes. Regrettably, some of the papers that were presented (Feferman, Klein, and Plotkin) could not be included in the present work due to timing problems. We nevertheless thank the authors for their contribu tion in terms of ideas and participation in the debate."

ThiscollectionofpapersstemsoriginallyfromaconferenceonProperty Theory, TypeTheoryandSemanticsheldinAmherstonMarch13-16 1986.The conference brought together logicians, philosophers, com puter scientists and linguists who had been working on these issues (often in isolation from one another).Ourintent wastoboostdebate and exchange of ideas on these fundamental issuesat a time ofrapid changeinsemanticsandcognitivescience. The paperspublished in thiswork have evolved substantially since their original presentation at the conference. Given their scope, we thought it convenient to divide the work into two volumes.The first deals primarily withlogicaland philosophical foundations, the second with more empirical semantic issues.Whilethere isa common set of issuestyingthetwovolumestogether, theyareboth self-containedand canbereadindependentlyofoneanother. Twoofthepapersinthepresentcollection(vanBentheminvolume Iand ChierchiainvolumeII)werenotactuallyread attheconference. They are nevertheless included here for their direct relevance to the topicsofthevolumes. Regrettably, some of the papers that were presented (Feferman, Klein, and Plotkin) could not be included in the presentwork due to timingproblems. Wenevertheless thank theauthorsfortheircontribu tionintermsofideasandparticipationinthedebate. The conference had a group of invited discussants whichincluded Emmon Bach, JanetFodor, Erhard Hinrichs, Angelika Kratzer, Fred Landman, Richard Larson, Godehard Link, Chris Menzel, Uwe Mon nich, andCarlPollard.Wethankthemall(alongwiththeotherpartici pants)fortheirstimulatingandlivelypresence."

This volume of papers grew outof a research project on "Cross-Linguistic Quantification" originated by Emmon Bach, Angelika Kratzer and Barbara Partee in 1987 at the University of Massachusetts at Amherst, and supported by National Science Foundation Grant BNS 871999. The publication also reflects directly or indirectly several other related activ ities. Bach, Kratzer, and Partee organized a two-evening symposium on cross-linguistic quantification at the 1988 Annual Meeting of the Linguistic Society of America in New Orleans (held without financial support) in order to bring the project to the attention of the linguistic community and solicit ideas and feedback from colleagues who might share our concern for developing a broader typological basis for research in semantics and a better integration of descriptive and theoretical work in the area of quantification in particular. The same trio organized a six-week workshop and open lecture series and related one-day confer ence on the same topic at the 1989 LSA Linguistic Institute at the University of Arizona in Tucson, supported by a supplementary grant, NSF grant BNS-8811250, and Partee offered a seminar on the same topic as part of the Institute course offerings. Eloise Jelinek, who served as a consultant on the principal grant and was a participant in the LSA symposium and the Arizona workshops, joined the group of editors for this volume in 1989."

This volume of papers grew outof a research project on "Cross-Linguistic Quantification" originated by Emmon Bach, Angelika Kratzer and Barbara Partee in 1987 at the University of Massachusetts at Amherst, and supported by National Science Foundation Grant BNS 871999. The publication also reflects directly or indirectly several other related activ ities. Bach, Kratzer, and Partee organized a two-evening symposium on cross-linguistic quantification at the 1988 Annual Meeting of the Linguistic Society of America in New Orleans (held without financial support) in order to bring the project to the attention of the linguistic community and solicit ideas and feedback from colleagues who might share our concern for developing a broader typological basis for research in semantics and a better integration of descriptive and theoretical work in the area of quantification in particular. The same trio organized a six-week workshop and open lecture series and related one-day confer ence on the same topic at the 1989 LSA Linguistic Institute at the University of Arizona in Tucson, supported by a supplementary grant, NSF grant BNS-8811250, and Partee offered a seminar on the same topic as part of the Institute course offerings. Eloise Jelinek, who served as a consultant on the principal grant and was a participant in the LSA symposium and the Arizona workshops, joined the group of editors for this volume in 1989."

1. 1 OBJECTIVES The main objective of this joint work is to bring together some ideas that have played central roles in two disparate theoretical traditions in order to con tribute to a better understanding of the relationship between focus and the syn tactic and semantic structure of sentences. Within the Prague School tradition and the branch of its contemporary development represented by Hajicova and Sgall (HS in the sequel), topic-focus articulation has long been a central object of study, and it has long been a tenet of Prague school linguistics that topic-focus structure has systematic relevance to meaning. Within the formal semantics tradition represented by Partee (BHP in the sequel), focus has much more recently become an area of concerted investigation, but a number of the semantic phenomena to which focus is relevant have been extensively investi gated and given explicit compositional semantic-analyses. The emergence of 'tripartite structures' (see Chapter 2) in formal semantics and the partial simi larities that can be readily observed between some aspects of tripartite structures and some aspects of Praguian topic-focus articulation have led us to expect that a closer investigation of the similarities and differences in these different theoretical constructs would be a rewarding undertaking with mutual benefits for the further development of our respective theories and potential benefit for the study of semantic effects of focus in other theories as well."

This volume of papers grew out of a research project on "Cross-Linguistic Quantification" originated by Emmon Bach, Angelika Kratzer and Barbara Partee in 1987 at the University of Massachusetts at Amherst, and supported by National Science Foundation Grant BNS 871999. The publication also reflects directly or indirectly several other related activ ities. Bach, Kratzer, and Partee organized a two-evening symposium on cross-linguistic quantification at the 1988 Annual Meeting of the Linguistic Society of America in New Orleans (held without financial support) in order to bring the project to the attention of the linguistic community and solicit ideas and feedback from colleagues who might share our concern for developing a broader typological basis for research in semantics and a better integration of descriptive and theoretical work in the area of quantification in particular. The same trio organized a six-week workshop and open lecture series and related one-day confer ence on the same topic at the 1989 LSA Linguistic Institute at the University of Arizona in Tucson, supported by a supplementary grant, NSF grant BNS-8811250, and Partee offered a seminar on the same topic as part of the Institute course offerings. Eloise Jelinek, who served as a consultant on the principal grant and was a participant in the LSA symposium and the Arizona workshops, joined the group of editors for this volume in 1989."

Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.

ThiscollectionofpapersstemsoriginallyfromaconferenceonProperty Theory, TypeTheoryandSemanticsheldinAmherstonMarch13-16 1986.The conference brought together logicians, philosophers, com puter scientists and linguists who had been working on these issues (often in isolation from one another).Ourintent wastoboostdebate and exchange of ideas on these fundamental issuesat a time ofrapid changeinsemanticsandcognitivescience. The paperspublished in thiswork have evolved substantially since their original presentation at the conference. Given their scope, we thought it convenient to divide the work into two volumes.The first deals primarily withlogicaland philosophical foundations, the second with more empirical semantic issues.Whilethere isa common set of issuestyingthetwovolumestogether, theyareboth self-containedand canbereadindependentlyofoneanother. Twoofthepapersinthepresentcollection(vanBentheminvolume Iand ChierchiainvolumeII)werenotactuallyread attheconference. They are nevertheless included here for their direct relevance to the topicsofthevolumes. Regrettably, some of the papers that were presented (Feferman, Klein, and Plotkin) could not be included in the presentwork due to timingproblems. Wenevertheless thank theauthorsfortheircontribu tionintermsofideasandparticipationinthedebate. The conference had a group of invited discussants whichincluded Emmon Bach, JanetFodor, Erhard Hinrichs, Angelika Kratzer, Fred Landman, Richard Larson, Godehard Link, Chris Menzel, Uwe Mon nich, andCarlPollard.Wethankthemall(alongwiththeotherpartici pants)fortheirstimulatingandlivelypresence."

This collection of papers stems originally from a conference on Property Theory, Type Theory and Semantics held in Amherst on March 13-16 1986. The conference brought together logicians, philosophers, com puter scientists and linguists who had been working on these issues (of ten in isolation from one another). Our intent was to boost debate and exchange of ideas on these fundamental issues at a time of rapid change in semantics and cognitive science. The papers published in this work have evolved substantially since their original presentation at the conference. Given their scope, we thought it convenient to divide the work into two volumes. The first deals primarily with logical and philosophical foundations, the second with more empirical semantic issues. While there is a common set of issues tying the two volumes together, they are both self-contained and can be read independently of one another. Two of the papers in the present collection (van Benthem in volume 1 and Chierchia in volume II) were not actually read at the conference. They are nevertheless included here for their direct relevance to the topics of the volumes. Regrettably, some of the papers that were presented (Feferman, Klein, and Plotkin) could not be included in the present work due to timing problems. We nevertheless thank the authors for their contribu tion in terms of ideas and participation in the debate."

Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.