Continuation Semantics Research Articles

Abstract Continuation Semantics for Multiparty Interactions in Process Calculi based on CCS

Abstract Continuation Semantics for Multiparty Interactions in Process Calculi based on CCS

Reachability in Continuous Pushdown VASS

Pushdown Vector Addition Systems with States (PVASS) consist of finitely many control states, a pushdown stack, and a set of counters that can be incremented and decremented, but not tested for zero. Whether the reachability problem is decidable for PVASS is a long-standing open problem. We consider continuous PVASS , which are PVASS with a continuous semantics. This means, the counter values are rational numbers and whenever a vector is added to the current counter values, this vector is first scaled with an arbitrarily chosen rational factor between zero and one. We show that reachability in continuous PVASS is NEXPTIME-complete. Our result is unusually robust: Reachability can be decided in NEXPTIME even if all numbers are specified in binary. On the other hand, NEXPTIME-hardness already holds for coverability, in fixed dimension, for bounded stack, and even if all numbers are specified in unary.

Discretisation and continuity: The emergence of symbols in communication

Vocal signalling systems, as used by humans and various non-human animals, exhibit discrete and continuous properties that can naturally be used to express discrete and continuous information, such as distinct words to denote objects in the world and prosodic features to convey the emotions of the speaker. However, continuous aspects are not always expressed with the continuous properties of an utterance but are frequently categorised into discrete symbols. While the existence of symbols in communication is self-evident, the emergence of discretisation from a continuous space is not well understood. In this paper, we investigate the emergence of discrete symbols in regions with a continuous semantics by simulating the learning process of two agents that acquire a shared signalling system. The task is formalised as a reinforcement learning problem with a continuous form and meaning space. We identify two causes for the emergence of discretisation that do not originate in discrete semantics: 1) premature convergence to sub-optimal signalling conventions and 2) topological mismatch between the continuous form space and the continuous semantic space. The insights presented in this paper shed light on the origins of discrete symbols, whose existence is assumed by a large body of research concerned with the emergence of syntactic structures and meaning in language.

CATEGORICAL SEMANTICS OF METRIC SPACES AND CONTINUOUS LOGIC

AbstractUsing the category of metric spaces as a template, we develop a metric analogue of the categorical semantics of classical/intuitionistic logic, and show that the natural notion of predicate in this “continuous semantics” is equivalent to the a priori separate notion of predicate in continuous logic, a logic which is independently well-studied by model theorists and which finds various applications. We show this equivalence by exhibiting the real interval $[0,1]$ in the category of metric spaces as a “continuous subobject classifier” giving a correspondence not only between the two notions of predicate, but also between the natural notion of quantification in the continuous semantics and the existing notion of quantification in continuous logic.Along the way, we formulate what it means for a given category to behave like the category of metric spaces, and afterwards show that any such category supports the aforementioned continuous semantics. As an application, we show that categories of presheaves of metric spaces are examples of such, and in fact even possess continuous subobject classifiers.

When redundancy is useful: A Bayesian approach to "overinformative" referring expressions.

Referring is one of the most basic and prevalent uses of language. How do speakers choose from the wealth of referring expressions at their disposal? Rational theories of language use have come under attack for decades for not being able to account for the seemingly irrational overinformativeness ubiquitous in referring expressions. Here we present a novel production model of referring expressions within the Rational Speech Act framework that treats speakers as agents that rationally trade off cost and informativeness of utterances. Crucially, we relax the assumption that informativeness is computed with respect to a deterministic Boolean semantics, in favor of a nondeterministic continuous semantics. This innovation allows us to capture a large number of seemingly disparate phenomena within one unified framework: the basic asymmetry in speakers' propensity to overmodify with color rather than size; the increase in overmodification in complex scenes; the increase in overmodification with atypical features; and the increase in specificity in nominal reference as a function of typicality. These findings cast a new light on the production of referring expressions: rather than being wastefully overinformative, reference is usefully redundant. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Continuation Semantics for Multi-Quantifier Sentences: Operation-Based Approaches

Classical scope-assignment strategies for multi-quantifier sentences involve quantifier phrase (QP)-movement. More recent continuation-based approaches provide a compelling alternative, for they interpret QP's in situ - without resorting to Logical Forms or any structures beyond the overt syntax. The continuation-based strategies can be divided into two groups: those that locate the source of scope-ambiguity in the rules of semantic composition and those that attribute it to the lexical entries for the quantifier words. In this paper, we focus on the former operation-based approaches and the nature of the semantic operations involved. More specifically, we discuss three such possible operation-based strategies for multi-quantifier sentences, together with their relative merits and costs.

Encryption and Information Network

Universal grammar assumes the existence of an innate structure common to all human languages. As with secret keys shared by two parties in cryptography, the innateness of language may be related to the continuity of language that both parties share. In other words, discrete language alone cannot construct continuous semantics, which therefore implies the innateness of continuity as proposed in universal grammar. This is also seen in the unique capacity to communicate quantum information, which contains continuity, using discrete language. On the other hand, ever since the development of quantum theory, its probabilistic nature during the measurement process has been debated, particularly by using the phenomenon of entanglement and nonlocality. Since a number of practical applications of quantum theory have been introduced more recently, various techniques of manipulating entanglement have been examined. In particular, it has been noted that for a given chain of non-maximal correlations, there exists a class of coefficients such that entanglement swapping yields the optimal result, namely the weakest link in the chain. A numerical comparison between the general coefficients and the optimal non-maximal states in the case of four and five 2-level entanglement is also provided.

SurvSurf: human retrieval on large surveillance video data

The volume of surveillance videos is increasing rapidly, where humans are the major objects of interest. Rapid human retrieval in surveillance videos is therefore desirable and applicable to a broad spectrum of applications. Existing big data processing tools that mainly target textual data cannot be applied directly for timely processing of large video data due to three main challenges: videos are more data-intensive than textual data; visual operations have higher computational complexity than textual operations; and traditional segmentation may damage video data's continuous semantics. In this paper, we design SurvSurf, a human retrieval system on large surveillance video data that exploits characteristics of these data and big data processing tools. We propose using motion information contained in videos for video data segmentation. The basic data unit after segmentation is called M-clip. M-clips help remove redundant video contents and reduce data volumes. We use the MapReduce framework to process M-clips in parallel for human detection and appearance/motion feature extraction. We further accelerate vision algorithms by processing only sub-areas with significant motion vectors rather than entire frames. In addition, we design a distributed data store called V-BigTable to structuralize M-clips' semantic information. V-BigTable enables efficient retrieval on a huge amount of M-clips. We implement the system on Hadoop and HBase. Experimental results show that our system outperforms basic solutions by one order of magnitude in computational time with satisfactory human retrieval accuracy.

A stable universal domain related to ω

In 1978, G. Plotkin noticed that $\mathbb{T}$ω, the cartesian product of ω copies of the three element flat domain of Booleans, is a universal domain, where ‘universal’ means that the retracts of $\mathbb{T}$ω for Scott's continuous semantics are exactly all the ωCC-domains, which with Scott continuous functions form a cartesian closed category. As usual, ‘ω’ is for ‘countably based,’ and here ‘CC’ is for ‘conditionally complete,’ which essentially means that any subset which is pairwise bounded has a least upper bound. Since $\mathbb{T}$ω is also an ωDI-domain (an important structure in stable domain theory), the following problem arises naturally: is there a cartesian closed category C of domains with stable functions such that $\mathbb{T}$ω, or a related structure, is universal in C for Berry’s stable semantics? The aim of this paper is to answer this question. We first investigate the properties of stable retracts. We introduce a new class of domains called conditionally complete DI-domains (CCDI-domain for short) and show that, (1) $\mathbb{T}$ω is an ωCCDI-domain and the category of CCDI-domains (resp. ωCCDI-domains) with stable functions is cartesian closed; (2) [$\mathbb{T}$ω →st$\mathbb{T}$ω] is a stable universal domain in the sense that every ωCCDI-domain is a stable retract of [$\mathbb{T}$ω → st$\mathbb{T}$ω], where [$\mathbb{T}$ω → st$\mathbb{T}$ω] is the stable function space of $\mathbb{T}$ω; (3) in particular, [$\mathbb{T}$ω → st$\mathbb{T}$ω] is not a stable retract of $\mathbb{T}$ω and hence $\mathbb{T}$ω is not universal for Berry’s stable semantics. We remark that this paper is a completion and correction of our earlier report in the Proceedings of the 6th International Symposium on Domain Theory and Its Applications (ISDT2013).

A Continuation Semantics of Interrogatives That Accounts for Baker's Ambiguity

No abstract.

Semantics‐Empowered Big Data Processing with Applications

We discuss the nature of big data and address the role of semantics in analyzing and processing big data that arises in the context of physical-cyber-social systems. To handle volume, we advocate semantic perception that can convert low-level observational data to higher-level abstractions more suitable for decision-making. To handle variety, we resort to semantic models and annotations of data so that intelligent processing can be done independent of heterogeneity of data formats and media. To handle velocity, we seek to use continuous semantics capability to dynamically create event or situation specific models and recognize relevant new concepts, entities and facts. To handle veracity, we explore trust models and approaches to glean trustworthiness. These four v's of big data are harnessed by the semantics-empowered analytics to derive value to support applications transcending physical-cyber-social continuum.

Sound and complete timed CTL model checking of timed Kripke structures and real-time rewrite theories

In this paper we show that the satisfaction of timed CTL (TCTL) formulas under the natural continuous semantics for both discrete-time and dense-time timed Kripke structures can be reduced to a model-checking problem in the pointwise semantics for a large class of timed Kripke structures, which includes many discrete-event systems. We then present a TCTL model checking algorithm for the pointwise case. An important consequence of our results is that they together describe a sound and complete TCTL model checking procedure for time-robust real-time rewrite theories also for dense time domains. We have implemented such a TCTL model checker for Real-Time Maude. Our model checker provides for free a sound and complete TCTL model checker for subsets of modeling languages, such as Ptolemy II and (Synchronous) AADL, which have Real-Time Maude analysis integrated into their tool environments.

Formula omitted] as a Stable Universal Domain

In the seventies, G. Plotkin noticed that Tω, the cartesian product of ω copies of the 3 elements flat domain of Boolean, is a universal domain, where “universal” means that the retracts of Tω in Scott's continuous semantics are exactly all the ωCC-domains, which with Scott continuous functions form a cartesian closed category. As usual “ω” is for “countably based”, and here “CC” is for “conditionally complete”, which essentially means that any subset which is pairwise bounded has an upper bound. Since Tω is also an ωDI-domain (an important structure in the stable domain theory), a problem arises naturally: Is Tω a universal domain for Berry's stable semantics? The aim of this paper is to answer this question. We investigate the properties of stable retracts and introduce a new domain named a conditionally complete DI-domain (a CCDI-domain for short). We show that, (1) a dcpo is a stable retract of Tω if and only if it is an ωCCDI-domain; (2) the category of ωCCDI-domain (resp. CCDI-domains) with stable functions is cartesian closed. So, the problem above has an affirmative answer.

Continuation Semantics for Asynchronous Concurrency

The paper presents a method of reasoning about the behaviour of asynchronous programs in denotational models designed with metric spaces and continuation semantics for concurrency.

Using Continuations to Account for Plural Quantification and Anaphora Binding

We give in this paper an explicit formal account of plural semantics in the framework of continuation semantics introduced in (1) and extended in (4). We deal with aspects of plural dynamic semantics such as plural quantification, plural anaphora, conjunction and disjunction, distributivity and maximality conditions. Those phenomena need no extra stipulations to be accounted for in this framework, because continuation semantics provides a unified account of scope- taking. Index Terms —Discourse semantics, continuations, plural anaphora, plural quantifiers' scope. I. INTRODUCTION HE formal study of plurals is a major and complex undertaking. It should address plural quantification, plural anaphora, conjunction and disjunction, distributivity, maximality, among other problems. Ideally, plural linguistic phenomena should be parallel to their singular counterpart. Unfortunately, it is not so: plurality introduces a number of complications not present in the analysis of singular. In this paper we will only give some directions for further study of plural semantics (our analysis is far from being exhaustive), with emphasis on plural anaphora, in the framework of continuation semantics. The programming language concept of continuations was successfully used by Barker and Shan in a series of articles to analyze intra-sentential linguistic phenomena such as focus fronting, donkey anaphora, presuppositions, crossover or superiority (2, 3, 19, 18, 1). Moreover, (9) proposed an elegant discourse semantics based on continuations. Continuations are a standard tool in computer science, used to control side effects of computation (such as evaluation order, print or passing values). The basic idea of continuizing a grammar is to provide subexpressions with direct access to their own continuations (future context), so subexpressions are modified to take a continuation as an argument. For instance, if we take the local context to be restricted to the sentence, when computing the meaning of the sentence John saw Mary , the default future of the value denoted by the subject is that it is destined to have the property of seeing Mary predicated of it. In symbols, the continuation of the subject denotation j is the function

On semantics of a term calculus for classical logic

The calculus of Curien and Herbelin was introduced to provide the Curry-Howard correspondence for classical logic. The terms of this calculus represent derivations in the sequent calculus proof system and reduction reflects the process of cut-elimination. We investigate some properties of two well-behaved subcalculi of untyped calculus of Curien and Herbelin, closed under the call-by-name and the call-by-value reduction, respectively. Continuation semantics is given using the category of negated domains and Moggi?s Kleisli category over predomains for the continuation monad. Soundness theorems are given for both versions thus relating operational and denotational semantics. A thorough overview of the work on continuation semantics is given.

Relating direct and predicate transformer partial correctness semantics for an imperative probabilistic-nondeterministic language

In Keimel et al. (2009) [5] we have systematically derived a predicate transformer semantics from a direct semantics in total correctness style for a nondeterministic/probabilistic basic imperative programming language L p . In the current paper we perform the analogous task starting from a direct semantics for L p in partial correctness style. As in [5] we establish a “Minkowski duality” providing an isomorphism between direct semantics and a continuation semantics from which a predicate transformer semantics wp a can be read off immediately. But wp a has only an auxiliary status and we use it to define a predicate transformer wlp as wlp ( P ) ( γ ) = 1 − wp a ( P ) ( 1 − γ ) capturing the idea of “weakest liberal preexpectation” (in analogy with weakest liberal precondition). We further explain why wlp of while-loops is computed as a greatest fixpoint and argue why this allows one to reason about while-loops in terms of invariants as opposed to the wp of while-loops as considered in [5] for which this is impossible.

Continuous Semantics to Analyze Real-Time Data

The traditional semantic approach has difficulties dealing with the dynamic domains involved in social, mobile, and sensor webs. Continuous semantics, which captures changing conceptualizations and relevant knowledge, can help us model those domains and analyze the related real-time data.

A Minkowski type duality mediating between state and predicate transformer semantics for a probabilistic nondeterministic language

In this paper we systematically derive a predicate transformer semantics from a direct semantics for a simple probabilistic-nondeterministic programming language L p . This goal is achieved by exhibiting the direct semantics as isomorphic to a continuation semantics from which the predicate transformer semantics can be read off immediately. This isomorphism allows one to identify nonempty convex compact saturated sets of valuations on the set S of states with certain “good” functionals from I S to I in a way similar to the one how H. Minkowski in 1903 related nonempty convex compact subsets of R n to what is nowadays called Minkowski functionals.

On the relations between monadic semantics

We present a simple computational metalanguage with general recursive types and multiple notions of effects, through which a variety of concrete denotational semantics can be conveniently factored, by suitably interpreting the effects as monads. We then propose a methodology for relating two such interpretations of the metalanguage, with the aim of showing that the semantics they induce agree for complete programs. As a prototypical instance of such a relation, we use the framework to show agreement between a direct and a continuation semantics of the simple, untyped functional language from Reynolds’s original paper on the subject.