Computational Adequacy Research Articles

The Representation of the Temporal Properties of Linguistic Utterances through a Mathematical Model

In this article we use a mathematical model to encode the temporal properties of linguistic utterances across languages by means of mathematical objects—points, lines, segments, vectors and versors—and the relations established among them in a four-dimensional space. Such temporal properties are encoded through threedifferent systems: tense—past, present and future—which locates the utterance on a temporal line, aspect—perfectivity and progressivity—which sets the viewpoint of the speaker, and Aktionsart, which refers to the structural temporal properties of the utterance such as telicity—whether the event has an endpoint or not—dynamicity—whether a change is conveyed or not—and duration. This model aims to be language independent in order to allow for the codification of the temporal properties of utterances in any language, thus rendering it appropriate to be used as an interlingua in Natural Language Processing (NLP) applications. This wouldsignificantly improve the comprehension of natural language in search engines and automatic translation systems, to name two examples. Hence, our ultimate goal is for this model to achieve computational adequacy.

Full abstraction for the quantum lambda-calculus

Quantum programming languages permit a hardware independent, high-level description of quantum algorithms. In particular, the quantum λ-calculus is a higher-order language with quantum primitives, mixing quantum data and classical control. Giving satisfactory denotational semantics to the quantum λ-calculus is a challenging problem that has attracted significant interest. In the past few years, both static (the quantum relational model) and dynamic (quantum game semantics) denotational models were given, with matching computational adequacy results. However, no model was known to be fully abstract. Our first contribution is a full abstraction result for the games model of the quantum λ-calculus. Full abstraction holds with respect to an observational quotient of strategies, obtained by summing valuations of all states matching a given observable. Our proof method for full abstraction extends a technique recently introduced to prove full abstraction for probabilistic coherence spaces with respect to probabilistic PCF. Our second contribution is an interpretation-preserving functor from quantum games to the quantum relational model, extending a long line of work on connecting static and dynamic denotational models. From this, it follows that the quantum relational model is fully abstract as well. Altogether, this gives a complete denotational landscape for the semantics of the quantum λ-calculus, with static and dynamic models related by a clean functorial correspondence, and both fully abstract.

An Evaluation Of A Linguistically Motivated Conversational Software Agent Framework

<p>This paper presents a critical evaluation framework for a linguistically motivated conversational software agent (CSA). The CSA prototype investigates the integration, intersection and interface of the language, knowledge, and speech act constructions (SAC) based on a grammatical object, and the sub-model of belief, desires and intention (BDI) and dialogue management (DM) for natural language processing (NLP). A long-standing issue within NLP CSA systems is refining the accuracy of interpretation to provide realistic dialogue to support human-to-computer communication. This prototype constitutes three phase models: (1) a linguistic model based on a functional linguistic theory – Role and Reference Grammar (RRG), (2) an Agent Cognitive Model with two inner models: (a) a knowledge representation model, (b) a planning model underpinned by BDI concepts, intentionality and rational interaction, and (3) a dialogue model. The evaluation strategy for this Java-based prototype is multi-approach driven by grammatical testing (English language utterances), software engineering and agent practice. A set of evaluation criteria are grouped per phase model, and the testing framework aims to test the interface, intersection and integration of all phase models. The empirical evaluations demonstrate that the CSA is a proof-of-concept, demonstrating RRG’s fitness for purpose for describing, and explaining phenomena, language processing and knowledge, and computational adequacy. Contrastingly, evaluations identify the complexity of lower level computational mappings of NL – agent to ontology with semantic gaps, and further addressed by a lexical bridging solution.</p>

A Higher-Order Calculus of Computational Fields

The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as an effective abstraction to fill the gap between the macro-level of such systems (specifying a system’s collective behaviour) and the micro-level (individual devices’ actions of computation and interaction to implement that collective specification), thereby providing a basis to better facilitate the engineering of collective APIs and complex systems at higher levels of abstraction. This article proposes a full formal foundation for field computations, in terms of a core (higher-order) calculus of computational fields containing a few key syntactic constructs, and equipped with typing, denotational and operational semantics. Critically, this allows formal establishment of a link between the micro- and macro-levels of collective adaptive systems by a result of computational adequacy and abstraction for the (aggregate) denotational semantics with respect to the (per-device) operational semantics.

Denotational semantics of recursive types in synthetic guarded domain theory

Just like any other branch of mathematics, denotational semantics of programming languages should be formalised in type theory, but adapting traditional domain theoretic semantics, as originally formulated in classical set theory to type theory has proven challenging. This paper is part of a project on formulating denotational semantics in type theories with guarded recursion. This should have the benefit of not only giving simpler semantics and proofs of properties such as adequacy, but also hopefully in the future to scale to languages with advanced features, such as general references, outside the reach of traditional domain theoretic techniques.Working inGuarded Dependent Type Theory(GDTT), we develop denotational semantics for Fixed Point Calculus (FPC), the simply typed lambda calculus extended with recursive types, modelling the recursive types of FPC using the guarded recursive types ofGDTT. We prove soundness and computational adequacy of the model inGDTTusing a logical relation between syntax and semantics constructed also using guarded recursive types. The denotational semantics is intensional in the sense that it counts the number of unfold-fold reductions needed to compute the value of a term, but we construct a relation relating the denotations of extensionally equal terms, i.e., pairs of terms that compute the same value in a different number of steps. Finally, we show how the denotational semantics of terms can be executed inside type theory and prove that executing the denotation of a boolean term computes the same value as the operational semantics of FPC.

Building an RRG computational grammar

Several grammatical models have shown a growing interest for the development of the conditions necessary to satisfy the so-called criterion of computational adequacy. Within Role and Reference Grammar (RRG [Van Valin & LaPolla, 1997; Van Valin, 2005; Pavey, 2010]), there have been some works seeking to implement the model in different computational environments (Diedrichsen, 2011, 2013; Guest, 2009; Nolan & Perinan-Pascual, 2014; Salem et al., 2008). In this scenario, the works of Van Valin & Mairal (2014), Perinan-Pascual (2013) and PerinanPascual & Arcas (2014) have set up the guidelines to devise a parsing system called ARTEMIS (Automatically Representing TExt Meaning via an InterlinguaBased System) for the computational treatment of the syntax and semantics of sentences. The goal of this paper is to contribute to the development of ARTEMIS focusing specifically on the design of the rules necessary for the effective computational parsing of unmarked simple clauses following the format of the Layered Structure of the Clause as described in RRG. Such rules should yield, as a result for every sentence, a parsed tree following the format of grammatical analyses in RRG.

Full abstraction for non-deterministic and probabilistic extensions of PCF I: The angelic cases

We examine several extensions and variants of Plotkin's language PCF, including non-deterministic and probabilistic choice constructs. For each, we give an operational and a denotational semantics, and compare them. In each case, we show soundness and computational adequacy: the two semantics compute the same values at ground types. Beyond this, we establish full abstraction (the observational preorder coincides with the denotational preorder) in a number of cases. In the probabilistic cases, this requires the addition of so-called statistical termination testers to the language.

On the Scope of Computational-and-Experimental Evaluation of the Seismic Adequacy of NPP Equipment

Relevant regulations require computational-and-experimental evaluation of the seismic adequacy of systems and equipment of each NPP unit, including the experimental study of the dynamic behavior of several thousand items of equipment in actual condition. Possible options for reducing the scope of equipment subject to visual checks, dynamic testing, and computational seismic adequacy analysis are examined. Procedures for optimizing the scope of the computational-and-experimental analysis of seismic adequacy are proposed.

Synthetic domain theory and models of linear Abadi & Plotkin logic

Plotkin suggested using a polymorphic dual intuitionistic/linear type theory ( PILL Y ) as a metalanguage for parametric polymorphism and recursion. In recent work the first two authors and R.L. Petersen have defined a notion of parametric LAPL-structure, which are models of PILL Y , in which one can reason using parametricity and, for example, solve a large class of domain equations, as suggested by Plotkin. In this paper, we show how an interpretation of a strict version of Bierman, Pitts and Russo’s language Lily into synthetic domain theory presented by Simpson and Rosolini gives rise to a parametric LAPL-structure. This adds to the evidence that the notion of LAPL-structure is a general notion, suitable for treating many different parametric models, and it provides formal proofs of consequences of parametricity expected to hold for the interpretation. Finally, we show how these results, in combination with Rosolini and Simpson’s computational adequacy result, can be used to prove consequences of parametricity for Lily . In particular, we show that one can solve domain equations in Lily up to ground contextual equivalence.

Logic-based automated multi-issue bilateral negotiation in peer-to-peer e-marketplaces

We present a novel logic-based framework to automate multi-issue bilateral negotiation in e-commerce settings. The approach exploits logic as communication language among agents, and optimization techniques in order to find Pareto-efficient agreements. We introduce $${\mathcal{P}}({\mathcal{N}})$$ , a propositional logic extended with concrete domains, which allows one to model relations among issues (both numerical and non-numerical ones) via logical entailment, differently from well-known approaches that describe issues as uncorrelated. Through $${\mathcal{P}}({\mathcal{N}})$$ it is possible to represent buyer's request, seller's supply and their respective preferences as formulas endowed with a formal semantics, e.g., if I spend more than 30000 � for a sedan then I want more than a two-years warranty and a GPS system included. We mix logic and utility theory in order to express preferences in a qualitative and quantitative way. We illustrate the theoretical framework, the logical language, the one-shot negotiation protocol we adopt, and show we are able to compute Pareto-efficient outcomes, using a mediator to solve an optimization problem. We prove the computational adequacy of our method by studying the complexity of the problem of finding Pareto-efficient solutions in our setting.

Denotational semantics of hybrid automata

We introduce a denotational semantics for non-linear hybrid automata and relate it to the operational semantics given in terms of hybrid trajectories. The semantics is defined as least fixpoint of an operator on the continuous domain of functions of time that take values in the lattice of compact subsets of n-dimensional Euclidean space. The semantic function assigns to every point in time the set of states the automaton can visit at that time, starting from one of its initial states. Our main results are the correctness and computational adequacy of the denotational semantics with respect to the operational semantics given in terms of hybrid trajectories. Moreover, we show that our denotational semantics can be effectively computed, which allows for the effective analysis of a large class of non-linear hybrid automata.

SUBSEXPL: a tool for simulating and comparing explicit substitutions calculi ★

We present the system SUBSEXPL used for simulating and comparing explicit substitutions calculi. The system allows the manipulation of expressions of the λ-calculus and of three different styles of explicit substitutions: the λσ, the λse and the suspension calculus. A variation of the suspension calculus, which allows for combination of steps of β-contraction is included too. Implementations of the η-reduction are provided for each style. Other explicit substitutions calculi can be easily incorporated into the system due to its modular structure. The uses of the system include: the visualization of the contractions of the λ-calculus in de Bruijn notation, and of guided one-step reductions as well as normalization via each of the associated substitution calculi. Many useful facilities are included: reductions can be easily recorded as text files, LATEX outputs can be generated and several examples for dealing with arithmetic operations and computational operators such as conditionals and repetitions in the λ-calculus are available. The system can be executed over Emacs using the x-symbol mode in such a way that λ-terms and terms of the explicit substitutions calculi are represented in its natural syntax avoiding the necessity of repeatedly generating LATEX outputs. The system has been of great help for systematically comparing explicit substitutions calculi, as well as for understanding properties of explicit substitutions such as the Preservation of Strong Normalization. In addition, it has been used for teaching basic properties of the λ-calculus such as: computational adequacy, the usefulness of de Bruijn's notation and of making explicit substitutions in real implementations.

Computational adequacy for recursive types in models of intuitionistic set theory

This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In contrast, as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models.

Imperative objects as mobile processes

An interpretation of Abadi and Cardelli's first-order Imperative ς- calculus into a typed π-calculus is presented. The interpretation validates the subtyping relation and the typing judgments of the ς-calculus, and is computationally adequate. The proof of computational adequacy makes use of (a π-calculus version) of ready simulation, and of a factorization of the interpretation into a functional part and a very simple imperative part. The interpretation can be extended to accommodate various type features. The interpretation can be used to compare and contrast the Imperative and the Functional ς-calculus, and to prove properties about them, within a unified framework.

Integration in Real PCF

Real PCF is an extension of the programming language PCF with a data type for real numbers. Although a Real PCF definable real number cannot be computed in finitely many steps, it is possible to compute an arbitrarily small rational interval containing the real number in a sufficiently large number of steps. Based on a domain-theoretic approach to integration, we propose two approaches to integration in Real PCF. One consists in adding integration as primitive. The other consists in adding a primitive for function maximization and then recursively defining integration from maximization. In both cases we have a computational adequacy theorem for the corresponding extension of Real PCF. Moreover, based on previous work on Real PCF definability, we show that Real PCF extended with the maximization operator is universal.

Classical logic, continuation semantics and abstract machines

One of the goals of this paper is to demonstrate that denotational semantics is useful for operational issues like implementation of functional languages by abstract machines. This is exemplified in a tutorial way by studying the case of extensional untyped call-by-name λ-calculus with Felleisen's control operator [Cscr ]. We derive the transition rules for an abstract machine from a continuation semantics which appears as a generalization of the ¬¬-translation known from logic. The resulting abstract machine appears as an extension of Krivine's machine implementing head reduction. Though the result, namely Krivine's machine, is well known our method of deriving it from continuation semantics is new and applicable to other languages (as e.g. call-by-value variants). Further new results are that Scott's D∞-models are all instances of continuation models. Moreover, we extend our continuation semantics to Parigot's λμ-calculus from which we derive an extension of Krivine's machine for λμ-calculus. The relation between continuation semantics and the abstract machines is made precise by proving computational adequacy results employing an elegant method introduced by Pitts.

Monte Carlo experiments and the defense of diffusion models in molecular population genetics

In the 1960s molecular population geneticists used Monte Carlo experiments to evaluate particular diffusion equation models. In this paper I examine the nature of this comparative evaluation and argue for three claims: first, Monte Carlo experiments are genuine experiments: second, Monte Carlo experiments can provide an important meansfor evaluating the adequacy of highly idealized theoretical models; and, third, the evaluation of the computational adequacy of a diffusion model with Monte Carlo experiments is significantlydifferent from the evaluation of the emperical adequacy of the same diffusion model.

Relational Properties of Domains

New tools are presented for reasoning about properties of recursively defined domains. We work within a general, category-theoretic framework for various notions of “relation” on domains and for actions of domain constructors on relations. Freyd's analysis of recursive types in terms of a property of mixed initiality/finality is transferred to a corresponding property ofinvariantrelations. The existence of invariant relations is proved under completeness assumptions about the notion of relation. We show how this leads to simpler proofs of the computational adequacy of denotational semantics for functional programming languages with user-declared datatypes. We show how the initiality/finality property of invariant relations can be specialized to yield an induction principle for admissible subsets of recursively defined domains, generalizing the principle of structural induction for inductively defined sets. We also show how the initiality/finality property gives rise to the co-induction principle studied by the author. [Theoret. Comput. Sci.124, 195–219 (1994)], by which equalities between elements of recursively defined domains may be proved via an appropriate notion of “bisimulation.”

Preservation of categorical knowledge in Alzheimer's disease: a computational account.

The distinction between knowledge of specific exemplars and knowledge of their general categories is central to much theorising on the nature of semantic memory. The dissociation between exemplar and category knowledge observed in Alzheimer's Disease (AD) would appear to support this distinction, and to suggest that different neural systems are involved in the representation of exemplar and category knowledge. We review the evidence for preserved category knowledge in the semantic memory impairment of AD, and propose an alternative interpretation, according to which category and exemplar knowledge are both represented in the same distributed neural substrate. The relative preservation of category knowledge is a consequence of the greater frequency, and hence greater robustness, of the representation of attributes shared by all or most members of a category, compared to exemplar-unique attributes. We test and confirm the computational adequacy of this hypothesis in two computer simulations.

Computational adequacy of the FIX-logic

This paper presents computational adequacy results for the FIX logical system introduced by Crole and Pitts in LICS'90. More precisely, we take two simple PCF style languages (whose dynamic semantics follow a call-by-value and call-by-name regime), give translations of the languages into suitable judgements in the FIX-logic and prove that the translations are adequate for the static and dynamic semantics. This shows that the FIX-logic can be regarded as a programming metalogic which will uniformly interpret both call-by-value and call-by-name languages. The proofs of dynamic adequacy make use of a logical relations technique which is based on the methods of Plotkin and Tait. We also show that there is some choice in the translation of recursion; certain translations make use of an existence property of the FIX-logic to prove computational adequacy.