Operational Semantics Research Articles

Unifying Model Execution and Deductive Verification with Interaction Trees in Isabelle/HOL

Model execution allows us to prototype and analyse software engineering models by stepping through their possible behaviours, using techniques like animation and simulation. On the other hand, deductive verification allows us to construct formal proofs demonstrating satisfaction of certain critical properties in support of high-assurance software engineering. To ensure coherent results between execution and proof, we need unifying semantics and automation. In this paper, we mechanise Interaction Trees (ITrees) in Isabelle/HOL to produce an execution and verification framework. ITrees are coinductive structures that allow us to encode infinite labelled transition systems, yet they are inherently executable. We use ITrees to create verification tools for stateful imperative programs, concurrent programs with message passing in the form of the CSP and Circus languages, and abstract system models in the style of the Z and B methods. We demonstrate how ITrees can account for diverse semantic presentations, such as structural operational semantics, a relational program model, and CSP's failures-divergences trace model. Finally, we demonstrate how ITrees can be executed using the Isabelle code generator to support the animation of models.

Intensional Functions

Functions in functional languages have a single elimination form — application — and cannot be compared, hashed, or subjected to other non-application operations. These operations can be approximated via defunctionalization: functions are replaced with first-order data and calls are replaced with invocations of a dispatch function. Operations such as comparison may then be implemented for these first-order data to approximate e.g. deduplication of continuations in algorithms such as unbounded searches. Unfortunately, this encoding is tedious, imposes a maintenance burden, and obfuscates the affected code. We introduce an alternative in intensional functions , a language feature which supports the definition of non-application operations in terms of a function’s definition site and closure-captured values. First-order data operations may be defined on intensional functions without burdensome code transformation. We give an operational semantics and type system and prove their formal properties. We further define intensional monads , whose Kleisli arrows are intensional functions, enabling monadic values to be similarly subjected to additional operations.

Hierarchical neural processing in γ oscillations for syntactic and semantic operations accounts for first- and second-language epistemology.

We discuss event-related power differences (ERPDs) in low- and broadband-γ oscillations as the embedded-clause edge is processed in wh-dependencies such as Which decision regarding/about him/her did Paul say that Lydie rejected without hesitation? in first (L1) and second language (L2) French speakers. The experimental conditions manipulated whether pronouns appeared in modifiers (Mods; regarding him/her) or in noun complements (Comps; about him/her) and whether they matched or mismatched a matrix-clause subject in gender. Across L1 and L2 speakers, we found that anaphora-linked ERPDs for Mods vs. Comps in evoked power first arose in low γ and then in broadband γ. Referential elements first seem to be retrieved from working memory by narrowband processes in low γ and then referential identification seems to be computed in broadband-γ output. Interactions between discourse- and syntax-based referential processes for the Mods vs. Comps in these ERPDs furthermore suggest that multidomain γ-band processing enables a range of elementary operations for discourse and semantic interpretation. We argue that a multidomain mechanism enabling operations conditioned by the syntactic and semantic nature of the elements processed interacts with local brain microcircuits representing features and feature sets that have been established in L1 or L2 acquisition, accounting for a single language epistemology across learning contexts.

Artificial Intelligence (AI) Challenges and Opportunities in Translation : An African Experience

The Artificial Intelligence (AI) revolution has become a reality in today’s world and its importance for linguistics was recognized very early. Despite its unprecedent surge and integration into various academic fields including language teaching and translation, surprisingly, little work has been done by scholars in advancing discussions on the profound impact of the AI on the diversity of widely available languages in both developed and developing world. Africa is linguistically diverse continent with about one third of the world’s languages that are vastly underrepresented in the global digital data pool. AI translation machine is supported in only 25 languages out of over 2000 languages in the continent. The paper deploys homomorphism model of AI theory to interrogate the natural language data drawn the African languages to present the current and future challenges, opportunities and potential for developing AI algorithms that could fit neatly into the translation of the African languages. Most of the discussions in the paper focuses on the seven patterns of the AI, the usage and implementation of AI algorithms in the translation science. The research findings show some of the complexities of the African languages in which their syntactic categories have multiple corresponding semantic objects. Unlike English, the findings also reveal that syntactic operation in the African languages do not always have one corresponding semantic operation as postulated by the homomorphism model of AI theory. the study contributes to scholarly literature by stressing the limits and opportunities that relate to using AI in translation science and supplying input from NLP algorithms practitioners to expand the AI applicability operation in the translation science.

A Logical Approach to Type Soundness

Type soundness, which asserts that “well-typed programs cannot go wrong”, is widely viewed as the canonical theorem one must prove to establish that a type system is doing its job. It is commonly proved using the so-called syntactic approach (aka progress and preservation ), which has had a huge impact on the study and teaching of programming language foundations. Unfortunately, syntactic type soundness is a rather weak theorem. It only applies to programs that are well-typed in their entirety, and thus tells us nothing about the many programs written in “safe” languages that make use of “unsafe” language features. Even worse, it tells us nothing about whether type systems achieve one of their main goals: enforcement of data abstraction. One can easily define a language that enjoys syntactic type soundness and yet fails to support even the most basic modular reasoning principles for abstraction mechanisms like closures, objects, and abstract data types. Given these concerns, we argue that programming languages researchers should no longer be satisfied with proving syntactic type soundness, and should instead start proving semantic type soundness , a more useful theorem which captures more accurately what type systems are actually good for. Semantic type soundness is an old idea—Milner’s original account of type soundness from 1978 was semantic—but it fell out of favor in the 1990s due to limitations and complexities of denotational models. In the succeeding decades, thanks to a series of technical advances—notably, step-indexed Kripke logical relations constructed over operational semantics, and higher-order concurrent separation logic as consolidated in the Iris framework in Coq—we can now build (machine-checked) semantic soundness proofs at a much higher level of abstraction than was previously possible. The resulting “logical” approach to semantic type soundness has already been employed to great effect in a number of recent papers, but those papers typically (a) concern advanced problem scenarios that complicate the presentation, (b) assume significant prior knowledge of the reader, and (c) suppress many details of the proofs. Here, we aim to provide a gentler, more pedagogically motivated introduction to logical type soundness, targeted at a broader audience that may or may not be familiar with logical relations and Iris. As a bonus, we also show how logical type soundness proofs can easily be generalized to establish an even stronger relational property— representation independence —for realistic type systems.

Exploring the Infinite Regress of Defining Words: A Critical Analysis of Semantic Methodologies

This article critically examines the concept of infinite regress in semantic methodologies and explores alternative approaches to understanding the meanings of words beyond traditional dictionary definitions. We delve into the strengths and limitations of dictionary-based semantics and contrast them with operational and contextual methodologies. Operational semantics, rooted in the works of P.W. Bridgman, and contextual approaches, which incorporate the influence of situational variables, offer more dynamic and adaptable frameworks for interpreting language. The implications of these methodologies for linguistic education and communication are thoroughly analyzed, highlighting the benefits of a more nuanced understanding of language in educational curricula and professional communication. This exploration advocates for a shift towards semantics that accommodate the fluid nature of language, encouraging a broader application of these theories in real-world settings.

A logical approach to graph databases

Graph databases are now playing an important role because they allow us to overcome some limitations of relational databases. In particular, in graph databases we are interested not only on the data contained but also on its topology. As a consequence, most graph database queries are navigational, asking whether some nodes are connected by edges or paths.Up to now, most foundational work has concentrated on the study of computational models and query languages, analyzing their expressivity, computability, and complexity. However, in our work we address a different kind of foundational work. We are not concerned with expressibility, efficiency or feasibility issues, but with correctness. More precisely, given an algorithm or an implementation for solving queries, how can we be sure that the answers obtained are correct (soundness) and that all possible correct answers are obtained by our implementation (completeness).In this sense, in this paper we first present a core query language, similar to Cypher or G-Core. Then, we define a simple logic whose formulas are precisely the database queries, and whose satisfaction relation defines what is a correct answer. Finally, we define an operational semantics, which could be seen as an abstract implementation of our language, showing that the semantics is correct, i.e. sound and complete with respect to our logic.

Towards a semantic blockchain: A behaviouristic approach to modelling Ethereum

Decentralised ledgers are gaining momentum following the interest of industries and people in smart contracts. Major attention is paid to blockchain applications intended for trading assets that exploit digital cryptographic certificates called tokens. Particularly relevant tokens are the non-fungible tokens (NFTs), namely, unique and non-replicable tokens used to represent the cryptographic counterpart of assets ranging from pieces of art through to licenses and certifications. A relevant consequence of the hard-coded nature of blockchains is the hardness of probing, in particular when advanced searchers involving the capabilities of the smart contracts or the assets digitised by NFTs are required. For this purpose, a formal representation for the operational semantics of smart contracts and of tokens has become particularly urgent, especially in economy and finance, where blockchains become increasingly relevant. Hence, we feel the need to tailor Semantic Web technologies to achieve that semantic representation at least for NFTS. This article reports on an ontology that leverages the Ontology for Agents, Systems, and Integration of Services (“OASIS”) towards the semantic representation of smart contracts responsible for managing ERC721-compliant NFTs and running on the Ethereum blockchain. Called Ether-OASIS, the proposed ontology adopts OASIS and tailors its behaviouristic approach to the Ethereum blockchain by conceiving smart contracts as agents running on the blockchain and, consequently, smart contract interactions as agent commitments. Smart contracts are represented in terms of their actions, purposes and tokens that they manage, thus realising a blockchain that is more usable both by users and automated applications. The ontology is evaluated using standard ontological metrics and applied on a case study concerning the minting and transferring of NFTs that digitise batches of wheat.

Trace Semantics for C++11 Memory Model

The C and C++ languages introduced the relaxed-memory concurrency into the language specification for efficiency purposes in 2011. Trace semantics can provide the mathematical foundation for the proposed C++11 memory model, and there is a lack of investigation of trace semantics for C++11. The Promising Semantics (PS) of Kang et al. provides the standard SC-style operational semantics for the C++11 concurrency model, where “SC” refers to “Sequential Consistency”. Inspired by PS, in this paper we first investigate the trace semantics for the relaxed read and write accesses under C++11, acting in the denotational semantics style. In our semantic model, a trace is in the form of a sequence of snapshots, and the snapshots record the modification in the relevant global or local variables, and the thread view. Moreover, the trace semantics for the release/acquire accesses under C++11 is also explored, based on the separated thread views and newly added message views. When considering this trace model, different accesses bring in their unique snapshots, and make distinguished effects on the production of the sequences. For any given program, the proposed trace semantics in this paper produces all the valid traces directly. Further, our trace semantics, together with that for TSO and MCA ARMv8, has the possibility to be the foundation of the meta model of the trace semantics for weak memory models.

A fresh look on semantics of Concurrent State Based Language (ConStaBL)

Statechart is a visual modelling language for systems. Our variant of the statechart has local variables, which interact significantly with the remainder of the language semantics. It allows arbitrary interleaving of concurrently executing action code, which allows more precise modelling of systems and upstream analysis of the same. We also establish the criteria based on our semantics for defining conflicting transitions and valid simulations. Our semantics do not allow transition conflicts in simulations and are stricter than most other available semantics of statecharts in that sense. In this paper, we extend the work on modular statecharts and present updated operational semantics with concurrency. We present the operational semantics in the form of the simulation algorithm. Our executable semantics can be used to simulate statechart models and verify their correctness. We present a preliminary setup to carry out fuzz testing of statechart models, an idea that does not have precedent in the literature to the best of our knowledge. We have used our simulator in conjunction with a well-known fuzzer to do fuzz testing of statechart models of non-trivial sizes and have found issues in them that would have been hard to find through inspection.

A Pure Demand Operational Semantics with Applications to Program Analysis

This paper develops a novel minimal-state operational semantics for higher-order functional languages that uses only the call stack and a source program point or a lexical level as the complete state information: there is no environment, no substitution, no continuation, etc. We prove this form of operational semantics equivalent to standard presentations. We then show how this approach can open the door to potential new applications: we define a program analysis as a direct finitization of this operational semantics. The program analysis that naturally emerges has a number of novel and interesting properties compared to standard program analyses for higher-order programs: for example, it can infer recurrences and does not need value widening. We both give a formal definition of the analysis and describe our current implementation.

Contributions of the left and right thalami to language: A meta-analytic approach.

Despite a pervasive cortico-centric view in cognitive neuroscience, subcortical structures including the thalamus have been shown to be increasingly involved in higher cognitive functions. Previous structural and functional imaging studies demonstrated cortico-thalamo-cortical loops which may support various cognitive functions including language. However, large-scale functional connectivity of the thalamus during language tasks has not been examined before. The present study employed meta-analytic connectivity modeling to identify language-related coactivation patterns of the left and right thalami. The left and right thalami were used as regions of interest to search the BrainMap functional database for neuroimaging experiments with healthy participants reporting language-related activations in each region of interest. Activation likelihood estimation analyses were then carried out on the foci extracted from the identified studies to estimate functional convergence for each thalamus. A functional decoding analysis based on the same database was conducted to characterize thalamic contributions to different language functions. The results revealed bilateral frontotemporal and bilateral subcortical (basal ganglia) coactivation patterns for both the left and right thalami, and also right cerebellar coactivations for the left thalamus, during language processing. In light of previous empirical studies and theoretical frameworks, the present connectivity and functional decoding findings suggest that cortico-subcortical-cerebellar-cortical loops modulate and fine-tune information transfer within the bilateral frontotemporal cortices during language processing, especially during production and semantic operations, but also other language (e.g., syntax, phonology) and cognitive operations (e.g., attention, cognitive control). The current findings show that the language-relevant network extends beyond the classical left perisylvian cortices and spans bilateral cortical, bilateral subcortical (bilateral thalamus, bilateral basal ganglia) and right cerebellar regions.

A Fibrational Tale of Operational Logical Relations: Pure, Effectful and Differential

Logical relations built on top of an operational semantics are one of the most successful proof methods in programming language semantics. In recent years, more and more expressive notions of operationally-based logical relations have been designed and applied to specific families of languages. However, a unifying abstract framework for operationally-based logical relations is still missing. We show how fibrations can provide a uniform treatment of operational logical relations, using as reference example a lambda-calculus with generic effects endowed with a novel, abstract operational semantics defined on a large class of categories. Moreover, this abstract perspective allows us to give a solid mathematical ground also to differential logical relations -- a recently introduced notion of higher-order distance between programs -- both pure and effectful, bringing them back to a common picture with traditional ones.

Progressive Text-to-Image Diffusion with Soft Latent Direction

In spite of the rapidly evolving landscape of text-to-image generation, the synthesis and manipulation of multiple entities while adhering to specific relational constraints pose enduring challenges. This paper introduces an innovative progressive synthesis and editing operation that systematically incorporates entities into the target image, ensuring their adherence to spatial and relational constraints at each sequential step. Our key insight stems from the observation that while a pre-trained text-to-image diffusion model adeptly handles one or two entities, it often falters when dealing with a greater number. To address this limitation, we propose harnessing the capabilities of a Large Language Model (LLM) to decompose intricate and protracted text descriptions into coherent directives adhering to stringent formats. To facilitate the execution of directives involving distinct semantic operations—namely insertion, editing, and erasing—we formulate the Stimulus, Response, and Fusion (SRF) framework. Within this framework, latent regions are gently stimulated in alignment with each operation, followed by the fusion of the responsive latent components to achieve cohesive entity manipulation. Our proposed framework yields notable advancements in object synthesis, particularly when confronted with intricate and lengthy textual inputs. Consequently, it establishes a new benchmark for text-to-image generation tasks, further elevating the field's performance standards.

Tarsis: An effective automata‐based abstract domain for string analysis

AbstractIn this paper, we introduce Tarsis, a new abstract domain based on the abstract interpretation theory that approximates string values through finite state automata. The main novelty of Tarsis is that it works over an alphabet of strings instead of single characters. On the one hand, such an approach requires a more complex and refined definition of the lattice operators and of the abstract semantics of string operators. On the other hand, it is in position to obtain strictly more precise results than state‐of‐the‐art approaches. We compare Tarsis both with simpler domains and with the standard automata model, targeting case studies containing standard yet challenging string manipulations. The performance gain w.r.t. the standard automata model is also assessed, measuring the speed‐up gained by Tarsis. Experiments confirm that Tarsis can obtain precise results without incurring in excessive computational costs.

RA-marking, delimitation, and TA-headed directional PPs in Persian

Abstract In this article, we examine the semantics of RA in Persian, focusing on the aspectual notion of delimitation. Delimitation is a term commonly used in the study of aspect and information structure. We distinguish between two functions of RA: as a semantic operator that measures delimited events involving mereological theme and incremental path verbs, and as an information-structural marker where RA serves as frame-setting accusative adjuncts. We also explore the aspectuality of RA in correlation with a motion construction involving a TA-headed goal phrase within the scope of RA. The motion event with TA, representing the vector, is rendered bounded through the influence of RA, indicating the endpoint of the path. Using Croft’s (2012) two-phase dimensional model of aspect, we demonstrate that TA and RA are both associated with delimitation, but operate on different axes of boundedness – TA on the qualitative axis and RA on the temporal axis.

Investigating the Impact of Semantic Operations on PersianSpeaking Aphasics: Further Evidence on the Localization View

Introduction: Broca and Wernicke’s patients perform satisfactorily regarding the processing of canonical syntactic structures, as maintained by previous studies; however, there has been a gap in the literature because no particular research has yet investigated the performance of these patients in the Persian circumstances once they were required to analyze sentences which would demand extra-semantic processing. This study clarifies the role of two critical semantic operations demanding extra-semantic processing at the sentential level: Aspectual coercion. It complements to provide some evidence on the localist view of the brain. Our rationale for selecting these operations was their pure semantic nature, not relying on morphosyntactic properties.
 Materials and Methods: Having recruited two age- and education-matched Broca, two Wernicke, and four healthy controls, we conducted a semantic judgment task in which the participants were asked to express their correct semantic judgment in the two coercion and two normal conditions.
 Results: Our results showed an approximately above-chance performance of the Broca group for all conditions; however, in the Wernicke group, the same result was not observed due to their poor performance in coercion conditions, though in ordinary sentences, they performed much better.
 Conclusion: Our findings, along with similar off-line and imaging studies, corroborate the view of localism, based on which Wernicke’s area is mainly responsible for the primary semantic operations while Broca’s area predominantly takes over syntactic parsing.

[formula omitted]JUpdate: An update language for time-varying JSON data

Time-varying JSON data are being used and exchanged in various today’s application frameworks like IoT platforms, Web services, cloud computing, online social networks, and mobile systems. However, in the state-of-the-art of JSON data management, there is neither a consensual nor a standard language for updating (i.e., inserting, modifying, and deleting) temporal JSON data, like the TSQL2 or SQL:2016 languages for temporal relational data. Moreover, existing JSON-based NoSQL DBMSs (e.g., MongoDB, Couchbase, CouchDB, OrientDB, and Riak) and both commercial relational DBMSs (e.g., IBM DB2 12, Oracle 19c, and MS SQL Server 2019) and open-source ones (e.g., PostgreSQL 15, and MySQL 8.0) supporting JSON documents do not provide any facility for maintaining temporal JSON data. Also in our previously proposed temporal JSON framework, called τJSchema, there was no feature for temporal JSON instance updates. For these reasons, we propose in this article a temporal update language, named τJUpdate (Temporal JUpdate), for JSON data in the τJSchema environment. We define it as a temporal extension of our previously introduced non-temporal JSON update language, named JUpdate (JSON Update). Both the syntax and the operational semantics of the data modification operations of JUpdate have been extended to support temporal aspects. τJUpdate allows to specify temporal JSON updates in an expressive and user-friendly manner, and to efficiently execute them in the τJSchema environment.

A Novel Semantic IoT Middleware for Secure Data Management: Blockchain and AI-Driven Context Awareness

In the modern digital landscape of the Internet of Things (IoT), data interoperability and heterogeneity present critical challenges, particularly with the increasing complexity of IoT systems and networks. Addressing these challenges, while ensuring data security and user trust, is pivotal. This paper proposes a novel Semantic IoT Middleware (SIM) for healthcare. The architecture of this middleware comprises the following main processes: data generation, semantic annotation, security encryption, and semantic operations. The data generation module facilitates seamless data and event sourcing, while the Semantic Annotation Component assigns structured vocabulary for uniformity. SIM adopts blockchain technology to provide enhanced data security, and its layered approach ensures robust interoperability and intuitive user-centric operations for IoT systems. The security encryption module offers data protection, and the semantic operations module underpins data processing and integration. A distinctive feature of this middleware is its proficiency in service integration, leveraging semantic descriptions augmented by user feedback. Additionally, SIM integrates artificial intelligence (AI) feedback mechanisms to continuously refine and optimise the middleware’s operational efficiency.

Quantum Bisimilarity via Barbs and Contexts: Curbing the Power of Non-deterministic Observers

Past years have seen the development of a few proposals for quantum extensions of process calculi. The rationale is clear: with the development of quantum communication protocols, there is a need to abstract and focus on the basic features of quantum concurrent systems, like CCS and CSP have done for their classical counterparts. So far, though, no accepted standard has emerged, neither for the syntax nor for the behavioural semantics. Indeed, the various proposals do not agree on what should be the observational properties of quantum values, and as a matter of fact, the soundness of such properties has never been validated against the prescriptions of quantum theory. To this aim, we introduce a new calculus, Linear Quantum CCS (lqCCS), and investigate the features of behavioural equivalences based on barbs and contexts. Our calculus can be thought of as an asynchronous, linear version of qCCS, which is in turn based on value-passing CCS. The combination of linearity and asynchronous communication fits well with the properties of quantum systems (e.g. the no-cloning theorem), since it ensures that each qubit is sent exactly once, precisely specifying which qubits of a process interact with the context. We exploit contexts to examine how bisimilarities relate to quantum theory. We show that the observational power of general contexts is incompatible with quantum theory: roughly, they can perform non-deterministic moves depending on quantum values without measuring (hence perturbing) them. Therefore, we refine the operational semantics in order to prevent contexts from performing unfeasible non-deterministic choices. This induces a coarser bisimilarity that better fits the quantum setting: (i) it lifts the indistinguishability of quantum states to the distributions of processes and, despite the additional constraints, (ii) it preserves the expressiveness of non-deterministic choices based on classical information. To the best of our knowledge, our semantics is the first one that satisfies the two properties above.