Expressing Discourse Dynamics Through Continuations Ekaterina Lebedeva
Total Page：16
File Type：pdf, Size：1020Kb
Load more
Recommended publications
-
Continuation-Passing Style
Continuation-Passing Style CS 6520, Spring 2002 1 Continuations and Accumulators In our exploration of machines for ISWIM, we saw how to explicitly track the current continuation for a computation (Chapter 8 of the notes). Roughly, the continuation reflects the control stack in a real machine, including virtual machines such as the JVM. However, accurately reflecting the \memory" use of textual ISWIM requires an implementation different that from that of languages like Java. The ISWIM machine must extend the continuation when evaluating an argument sub-expression, instead of when calling a function. In particular, function calls in tail position require no extension of the continuation. One result is that we can write \loops" using λ and application, instead of a special for form. In considering the implications of tail calls, we saw that some non-loop expressions can be converted to loops. For example, the Scheme program (define (sum n) (if (zero? n) 0 (+ n (sum (sub1 n))))) (sum 1000) requires a control stack of depth 1000 to handle the build-up of additions surrounding the recursive call to sum, but (define (sum2 n r) (if (zero? n) r (sum2 (sub1 n) (+ r n)))) (sum2 1000 0) computes the same result with a control stack of depth 1, because the result of a recursive call to sum2 produces the final result for the enclosing call to sum2 . Is this magic, or is sum somehow special? The sum function is slightly special: sum2 can keep an accumulated total, instead of waiting for all numbers before starting to add them, because addition is commutative. -
Denotational Semantics
Denotational Semantics CS 6520, Spring 2006 1 Denotations So far in class, we have studied operational semantics in depth. In operational semantics, we define a language by describing the way that it behaves. In a sense, no attempt is made to attach a “meaning” to terms, outside the way that they are evaluated. For example, the symbol ’elephant doesn’t mean anything in particular within the language; it’s up to a programmer to mentally associate meaning to the symbol while defining a program useful for zookeeppers. Similarly, the definition of a sort function has no inherent meaning in the operational view outside of a particular program. Nevertheless, the programmer knows that sort manipulates lists in a useful way: it makes animals in a list easier for a zookeeper to find. In denotational semantics, we define a language by assigning a mathematical meaning to functions; i.e., we say that each expression denotes a particular mathematical object. We might say, for example, that a sort implementation denotes the mathematical sort function, which has certain properties independent of the programming language used to implement it. In other words, operational semantics defines evaluation by sourceExpression1 −→ sourceExpression2 whereas denotational semantics defines evaluation by means means sourceExpression1 → mathematicalEntity1 = mathematicalEntity2 ← sourceExpression2 One advantage of the denotational approach is that we can exploit existing theories by mapping source expressions to mathematical objects in the theory. The denotation of expressions in a language is typically defined using a structurally-recursive definition over expressions. By convention, if e is a source expression, then [[e]] means “the denotation of e”, or “the mathematical object represented by e”. -
Proceedings of the Textinfer 2011 Workshop on Applied Textual
EMNLP 2011 TextInfer 2011 Workshop on Textual Entailment Proceedings of the Workshop July 30, 2011 Edinburgh, Scotland, UK c 2011 The Association for Computational Linguistics Order copies of this and other ACL proceedings from: Association for Computational Linguistics (ACL) 209 N. Eighth Street Stroudsburg, PA 18360 USA Tel: +1-570-476-8006 Fax: +1-570-476-0860 [email protected] ISBN 978-1-937284-15-2 / 1-937284-15-8 ii Introduction Textual inference and paraphrase have attracted a significant amount of attention in recent years. Many NLP tasks, including question answering, information extraction, and text summarization, can be mapped at least partially onto the recognition of textual entailments and the detection of semantic equivalence between texts. Robust and accurate algorithms and resources for inference and paraphrasing can be beneficial for a broad range of NLP applications, and have stimulated research in the area of applied semantics over the last years. The success of the Recognizing Textual Entailment challenges and the high participation in previous workshops on textual inference and paraphrases – Empirical Modeling of Semantic Equivalence and Entailment (ACL 2005), Textual Entailment and Paraphrasing (ACL/PASCAL 2007), and TextInfer 2009 (ACL) – show that there is substantial interest in the area among the research community. TextInfer 2011 follows these workshops and aims to provide a common forum for researchers to discuss and compare novel ideas, models and tools for textual inference and paraphrasing. One particular goal is to broaden the workshop to invite both theoretical and applied research contributions on the joint topic of “inference.” We aim to bring together empirical approaches, which have tended to dominate previous textual entailment events, with formal approaches to inference, which are more often presented at events like ICoS or IWCS. -
Referential Dependencies Between Conflicting Attitudes
J Philos Logic DOI 10.1007/s10992-016-9397-7 Referential Dependencies Between Conflicting Attitudes Emar Maier1 Received: 18 June 2015 / Accepted: 23 March 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract A number of puzzles about propositional attitudes in semantics and phi- losophy revolve around apparent referential dependencies between different attitudes within a single agent’s mental state. In a series of papers, Hans Kamp (2003. 2015) offers a general framework for describing such interconnected attitude complexes, building on DRT and dynamic semantics. I demonstrate that Kamp’s proposal cannot deal with referential dependencies between semantically conflicting attitudes, such as those in Ninan’s (2008) puzzle about de re imagination. To solve the problem I propose to replace Kamp’s treatment of attitudes as context change potentials with a two-dimensional analysis. Keywords Propositional attitudes · Hans Kamp · Ninan’s puzzle · DRT · Dynamic semantics 1 Three puzzles about dependent attitudes Detective Mary investigates a mysterious death. She thinks the deceased was mur- dered and she hopes that the murderer is soon caught and arrested. A standard Emar Maier [email protected] 1 University of Groningen, Oude Boteringestraat 52, 9712GL Groningen, The Netherlands E. Maier analysis of definite descriptions and of hope as a propositional attitude gives us two different ways of characterizing Mary’s hope that the murderer is arrested (Quine [24]):1 ∃ ∀ ↔ = ∧ (1) a. de dicto : HOPE m x y murderer(y) x y arrested(x) b. de re : ∃x ∀y murderer(y) ↔ x = y ∧ HOPEmarrested(x) Neither of these logical forms captures what’s going on in the scenario. -
A Descriptive Study of California Continuation High Schools
Issue Brief April 2008 Alternative Education Options: A Descriptive Study of California Continuation High Schools Jorge Ruiz de Velasco, Greg Austin, Don Dixon, Joseph Johnson, Milbrey McLaughlin, & Lynne Perez Continuation high schools and the students they serve are largely invisible to most Californians. Yet, state school authorities estimate This issue brief summarizes that over 115,000 California high school students will pass through one initial findings from a year- of the state’s 519 continuation high schools each year, either on their long descriptive study of way to a diploma, or to dropping out of school altogether (Austin & continuation high schools in 1 California. It is the first in a Dixon, 2008). Since 1965, state law has mandated that most school series of reports from the on- districts enrolling over 100 12th grade students make available a going California Alternative continuation program or school that provides an alternative route to Education Research Project the high school diploma for youth vulnerable to academic or conducted jointly by the John behavioral failure. The law provides for the creation of continuation W. Gardner Center at Stanford University, the schools ‚designed to meet the educational needs of each pupil, National Center for Urban including, but not limited to, independent study, regional occupation School Transformation at San programs, work study, career counseling, and job placement services.‛ Diego State University, and It contemplates more intensive services and accelerated credit accrual WestEd. strategies so that students whose achievement in comprehensive schools has lagged might have a renewed opportunity to ‚complete the This project was made required academic courses of instruction to graduate from high school.‛ 2 possible by a generous grant from the James Irvine Taken together, the size, scope and legislative design of the Foundation. -
RELATIONAL PARAMETRICITY and CONTROL 1. Introduction the Λ
Logical Methods in Computer Science Vol. 2 (3:3) 2006, pp. 1–22 Submitted Dec. 16, 2005 www.lmcs-online.org Published Jul. 27, 2006 RELATIONAL PARAMETRICITY AND CONTROL MASAHITO HASEGAWA Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502 Japan, and PRESTO, Japan Science and Technology Agency e-mail address: [email protected] Abstract. We study the equational theory of Parigot’s second-order λµ-calculus in con- nection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the relational parametricity on the tar- get calculus induces a natural notion of equivalence on the λµ-terms. On the other hand, the unconstrained relational parametricity on the λµ-calculus turns out to be inconsis- tent. Following these facts, we propose to formulate the relational parametricity on the λµ-calculus in a constrained way, which might be called “focal parametricity”. Dedicated to Prof. Gordon Plotkin on the occasion of his sixtieth birthday 1. Introduction The λµ-calculus, introduced by Parigot [26], has been one of the representative term calculi for classical natural deduction, and widely studied from various aspects. Although it still is an active research subject, it can be said that we have some reasonable un- derstanding of the first-order propositional λµ-calculus: we have good reduction theories, well-established CPS semantics and the corresponding operational semantics, and also some canonical equational theories enjoying semantic completeness [16, 24, 25, 36, 39]. The last point cannot be overlooked, as such complete axiomatizations provide deep understand- ing of equivalences between proofs and also of the semantic structure behind the syntactic presentation. -
Continuation Calculus
Eindhoven University of Technology MASTER Continuation calculus Geron, B. Award date: 2013 Link to publication Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain Continuation calculus Master’s thesis Bram Geron Supervised by Herman Geuvers Assessment committee: Herman Geuvers, Hans Zantema, Alexander Serebrenik Final version Contents 1 Introduction 3 1.1 Foreword . 3 1.2 The virtues of continuation calculus . 4 1.2.1 Modeling programs . 4 1.2.2 Ease of implementation . 5 1.2.3 Simplicity . 5 1.3 Acknowledgements . 6 2 The calculus 7 2.1 Introduction . 7 2.2 Definition of continuation calculus . 9 2.3 Categorization of terms . 10 2.4 Reasoning with CC terms . -
6.5 a Continuation Machine
6.5. A CONTINUATION MACHINE 185 6.5 A Continuation Machine The natural semantics for Mini-ML presented in Chapter 2 is called a big-step semantics, since its only judgment relates an expression to its final value—a “big step”. There are a variety of properties of a programming language which are difficult or impossible to express as properties of a big-step semantics. One of the central ones is that “well-typed programs do not go wrong”. Type preservation, as proved in Section 2.6, does not capture this property, since it presumes that we are already given a complete evaluation of an expression e to a final value v and then relates the types of e and v. This means that despite the type preservation theorem, it is possible that an attempt to find a value of an expression e leads to an intermediate expression such as fst z which is ill-typed and to which no evaluation rule applies. Furthermore, a big-step semantics does not easily permit an analysis of non-terminating computations. An alternative style of language description is a small-step semantics.Themain judgment in a small-step operational semantics relates the state of an abstract machine (which includes the expression to be evaluated) to an immediate successor state. These small steps are chained together until a value is reached. This level of description is usually more complicated than a natural semantics, since the current state must embody enough information to determine the next and all remaining computation steps up to the final answer. -
Compositional Semantics for Composable Continuations from Abortive to Delimited Control
Compositional Semantics for Composable Continuations From Abortive to Delimited Control Paul Downen Zena M. Ariola University of Oregon fpdownen,[email protected] Abstract must fulfill. Of note, Sabry’s [28] theory of callcc makes use of Parigot’s λµ-calculus, a system for computational reasoning about continuation variables that have special properties and can only be classical proofs, serves as a foundation for control operations em- instantiated by callcc. As we will see, this not only greatly aids in bodied by operators like Scheme’s callcc. We demonstrate that the reasoning about terms with free variables, but also helps in relating call-by-value theory of the λµ-calculus contains a latent theory of the equational and operational interpretations of callcc. delimited control, and that a known variant of λµ which unshack- In another line of work, Parigot’s [25] λµ-calculus gives a sys- les the syntax yields a calculus of composable continuations from tem for computing with classical proofs. As opposed to the pre- the existing constructs and rules for classical control. To relate to vious theories based on the λ-calculus with additional primitive the various formulations of control effects, and to continuation- constants, the λµ-calculus begins with continuation variables in- passing style, we use a form of compositional program transforma- tegrated into its core, so that control abstractions and applications tions which preserves the underlying structure of equational the- have the same status as ordinary function abstraction. In this sense, ories, contexts, and substitution. Finally, we generalize the call- the λµ-calculus presents a native language of control. -
Analyticity, Necessity and Belief Aspects of Two-Dimensional Semantics
!"# #$%"" &'( ( )#"% * +, %- ( * %. ( %/* %0 * ( +, %. % +, % %0 ( 1 2 % ( %/ %+ ( ( %/ ( %/ ( ( 1 ( ( ( % "# 344%%4 253333 #6#787 /0.' 9'# 86' 8" /0.' 9'# 86' (#"8'# Analyticity, Necessity and Belief Aspects of two-dimensional semantics Eric Johannesson c Eric Johannesson, Stockholm 2017 ISBN print 978-91-7649-776-0 ISBN PDF 978-91-7649-777-7 Printed by Universitetsservice US-AB, Stockholm 2017 Distributor: Department of Philosophy, Stockholm University Cover photo: the water at Petite Terre, Guadeloupe 2016 Contents Acknowledgments v 1 Introduction 1 2 Modal logic 7 2.1Introduction.......................... 7 2.2Basicmodallogic....................... 13 2.3Non-denotingterms..................... 21 2.4Chaptersummary...................... 23 3 Two-dimensionalism 25 3.1Introduction.......................... 25 3.2Basictemporallogic..................... 27 3.3 Adding the now operator.................. 29 3.4Addingtheactualityoperator................ 32 3.5 Descriptivism ......................... 34 3.6Theanalytic/syntheticdistinction............. 40 3.7 Descriptivist 2D-semantics .................. 42 3.8 Causal descriptivism ..................... 49 3.9Meta-semantictwo-dimensionalism............. 50 3.10Epistemictwo-dimensionalism................ 54 -
Lecture 6. Dynamic Semantics, Presuppositions, and Context Change, II
Formal Semantics and Formal Pragmatics, Lecture 6 Formal Semantics and Formal Pragmatics, Lecture 6 Barbara H. Partee, MGU, April 10, 2009 p. 1 Barbara H. Partee, MGU, April 10, 2009 p. 2 Lecture 6. Dynamic Semantics, Presuppositions, and Context Change, II. DR (1) (incomplete) 1.! Kamp’s Discourse Representation Theory............................................................................................................ 1! u v 2.! File Change Semantics and the Anaphoric Theory of Definiteness: Heim Chapter III ........................................ 5! ! ! 2.1. Informative discourse and file-keeping. ........................................................................................................... 6! 2.2. Novelty and Familiarity..................................................................................................................................... 9! Pedro owns a donkey 2.3. Truth ................................................................................................................................................................ 10! u = Pedro 2.4. Conclusion: Motivation for the File Change Model of Semantics.................................................................. 10! u owns a donkey 3. Presuppositions and their parallels to anaphora ..................................................................................................... 11! donkey (v) 3.1. Background on presuppositions ..................................................................................................................... -
Accumulating Bindings
Accumulating bindings Sam Lindley The University of Edinburgh [email protected] Abstract but sums apparently require the full power of ap- plying a single continuation multiple times. We give a Haskell implementation of Filinski’s nor- malisation by evaluation algorithm for the computational In my PhD thesis I observed [14, Chapter 4] that by gen- lambda-calculus with sums. Taking advantage of extensions eralising the accumulation-based interpretation from a list to the GHC compiler, our implementation represents object to a tree that it is possible to use an accumulation-based language types as Haskell types and ensures that type errors interpretation for normalising sums. There I focused on are detected statically. an implementation using the state supported by the inter- Following Filinski, the implementation is parameterised nal monad of the metalanguage. The implementation uses over a residualising monad. The standard residualising Huet’s zipper [13] to navigate a mutable binding tree. Here monad for sums is a continuation monad. Defunctionalising we present a Haskell implementation of normalisation by the uses of the continuation monad we present the binding evaluation for the computational lambda calculus using a tree monad as an alternative. generalisation of Filinski’s binding list monad to incorpo- rate a tree rather than a list of bindings. (One motivation for using state instead of continuations 1 Introduction is performance. We might expect a state-based implementa- tion to be faster than an alternative delimited continuation- Filinski [12] introduced normalisation by evaluation for based implementation. For instance, Sumii and Kobay- the computational lambda calculus, using layered mon- ishi [17] claim a 3-4 times speed-up for state-based versus ads [11] for formalising name generation and for collecting continuation-based let-insertion.