Polymorphic scenario-based specification models: semantics and applications

We present polymorphic scenarios, a generalization of a UML2-compliant variant of Damm and Harel??s live sequence charts (LSC) in the context of object-orientation. Polymorphic scenarios are visualized using (modal) sequence diagrams where lifelines may represent classes and interfaces rather than concrete objects. Their semantics takes advantage of inheritance and interface realization to allow the specification of most expressive, succinct, and reusable universal and existential inter-object scenarios for object-oriented system models. We motivate the use of polymorphic scenarios, formally define their trace-based semantics, and present their application for scenario-based testing and execution, as implemented in the S2A compiler developed at the Weizmann Institute of Science. We further discuss advanced semantic issues arising from the use of scenarios in a polymorphic setting, suggest possible extensions, present a UML profile to support polymorphic scenarios, consider the application of the polymorphic semantics to other variants of scenario-based specification languages, and position our work in the broader context of behavioral subtyping.     

Hybrid

Combining higher-order abstract syntax and (co)-induction in a logical framework is well known to be problematic. We describe the theory and the practice of a tool called Hybrid, within Isabelle/HOL and Coq, which aims to address many of these difficulties. It allows object logics to be represented using higher-order abstract syntax, and reasoned about using tactical theorem proving and principles of (co)induction. Moreover, it is definitional, which guarantees consistency within a classical type theory. The idea is to have a de Bruijn representation of λ-terms providing a definitional layer that allows the user to represent object languages using higher-order abstract syntax, while offering tools for reasoning about them at the higher level. In this paper we describe how to use Hybrid in a multi-level reasoning fashion, similar in spirit to other systems such as Twelf and Abella. By explicitly referencing provability in a middle layer called a specification logic, we solve the problem of reasoning by (co)induction in the presence of non-stratifiable hypothetical judgments, which allow very elegant and succinct specifications of object logic inference rules. We first demonstrate the method on a simple example, formally proving type soundness (subject reduction) for a fragment of a pure functional language, using a minimal intuitionistic logic as the specification logic. We then prove an analogous result for a continuation-machine presentation of the operational semantics of the same language, encoded this time in an ordered linear logic that serves as the specification layer. This example demonstrates the ease with which we can incorporate new specification logics, and also illustrates a significantly more complex object logic whose encoding is elegantly expressed using features of the new specification logic.     

A compositional semantics of UML-RSDS

This paper provides a semantics for the UML-RSDS (Reactive System Development Support) subset of UML, using the real-time action logic (RAL) formalism. We show how this semantics can be used to resolve some ambiguities and omissions in UML semantics, and to support reasoning about specifications using the B formal method and tools. We use ‘semantic profiles’ to provide precise semantics for different semantic variation points of UML. We also show how RAL can be used to give a semantics to notations for real-time specification in UML. Unlike other approaches to UML semantics, which concentrate on the class diagram notation, our semantic representation has behaviour as a central element, and can be used to define semantics for use cases, state machines and interactions, in addition to class diagrams.     

True-concurrency probabilistic models: Branching cells and distributed probabilities for event structures

This paper is devoted to probabilistic models for concurrent systems under their true-concurrency semantics. Here we address probabilistic event structures. We consider a new class of event structures, called locally finite, that extend confusion-free event structure. In locally finite event structures, maximal configurations can be tiled with branching cells: branching cells are minimal and finite sub-structures capturing the choices performed while scanning a maximal configuration. The probabilistic event structures that we introduce have the property that “concurrent processes are independent in the probabilistic sense.”     

Logical approximation for program analysis

The abstract interpretation of programs relates the exact semantics of a programming language to a finite approximation of those semantics. In this article, we describe an approach to abstract interpretation that is based in logic and logic programming. Our approach consists of faithfully representing a transition system within logic and then manipulating this initial specification to create a logical approximation of the original specification. The objective is to derive a logical approximation that can be interpreted as a terminating forward-chaining logic program; this ensures that the approximation is finite and that, furthermore, an appropriate logic programming interpreter can implement the derived approximation. We are particularly interested in the specification of the operational semantics of programming languages in ordered logic, a technique we call substructural operational semantics (SSOS). We show that manifestly sound control flow and alias analyses can be derived as logical approximations of the substructural operational semantics of relevant languages.     

On the autoepistemic reconstruction of logic programming

Current semantics of logic programs normally ignore thesyntactical aspects of the programs. As a result, only the meanings ofsome well-behaved programs can be captured by these semantics. In this paper however, we propose a new semantics of logic programs that can reflectsome of the syntactical behaviours of the programs. The central notion of the semantics is the concept of aneutral clause p ← A which does not affect the behaviour of p in a program. The logic that underlies the semantics is based on anintensional extension of Levesque’s autoepistemicpredicate logic. It differs from existing autoepistemic logics in that it isquantificational andconstructive. We will also compare and contrast our semantics with some well-known semantics. In particular, we will show how to capture the undefined value of a logic program without resorting to a three-valued nonmonotonic formalism. This is achieved by translating an incoherent AE logic program to a program with multiple AE extensions whose intersection can then be used to characterize the undefined value of a logic program.     

Towards Behavioral Maude: Behavioral Membership Equational Logic

How can algebraic and coalgebraic specifications be integrated? How can behavioral equivalence be addressed in an algebraic specification language? The hidden-sorted approach, originating in work of Goguen and Meseguer in the early 80's, and further developed into the hidden-sorted logic approach by researchers at Oxford, UC San Diego, and Kanazawa offers some attractive answers, and has been implemented in both BOBJ and CafeOBJ. In this work we investigate both further extensions of hidden logic, and an extension of the Maude specification language called BMaude supporting this extended hidden-sorted semantics.Maude's underlying equational logic, membership equational logic, generalizes and increases the expressive power of many-sorted and order-sorted equational logics. We develop a hidden-sorted extension of membership equational logic, and give conditions under which theories have both an algebraic and a coalgebraic semantics, including final (co-)algebras. We also discuss the language design of BMaude, based on such an extended logic and using categorical notions in and across the different institutions involved. We also explain how Maude's reflective semantics provides a systematic method to extend Maude to BMaude within Maude, including module composition operations, evaluation, and automated proof methods.     

A formal framework for software product lines

ContextA Software Product Line is a set of software systems that are built from a common set of features. These systems are developed in a prescribed way and they can be adapted to fit the needs of customers. Feature models specify the properties of the systems that are meaningful to customers. A semantics that models the feature level has the potential to support the automatic analysis of entire software product lines.ObjectiveThe objective of this paper is to define a formal framework for Software Product Lines. This framework needs to be general enough to provide a formal semantics for existing frameworks like FODA (Feature Oriented Domain Analysis), but also to be easily adaptable to new problems.MethodWe define an algebraic language, called SPLA, to describe Software Product Lines. We provide the semantics for the algebra in three different ways. The approach followed to give the semantics is inspired by the semantics of process algebras. First we define an operational semantics, next a denotational semantics, and finally an axiomatic semantics. We also have defined a representation of the algebra into propositional logic.ResultsWe prove that the three semantics are equivalent. We also show how FODA diagrams can be automatically translated into SPLA. Furthermore, we have developed our tool, called AT, that implements the formal framework presented in this paper. This tool uses a SAT-solver to check the satisfiability of an SPL.ConclusionThis paper defines a general formal framework for software product lines. We have defined three different semantics that are equivalent; this means that depending on the context we can choose the most convenient approach: operational, denotational or axiomatic. The framework is flexible enough because it is closely related to process algebras. Process algebras are a well-known paradigm for which many extensions have been defined.     

Declarative semantics of transactions in ORM

In order to specify databases completely at the conceptual level, conceptual database specification languages should contain a data definition (sub)language (DDL), for specifying data structures (+constraints), a data retrieval (sub)language (DRL), for specifying queries, as well as a (declarative) data manipulation (sub)language (DML), for specifying transactions.Object Role Modeling (ORM) is a powerful method for designing and querying database models at the conceptual level. By means of verbalization the application is also described in natural language as used by domain experts, for communication and validation purposes. ORM currently comprises a DDL and a DRL (ConQuer). However, the ORM-method does not yet contain an expressive DML for specifying transactions at the conceptual level.In an earlier paper we designed a syntactic extension of the ORM-method with a DML for specifying transactions at the conceptual level in a purely declarative way. For all transactions we proposed syntaxes, verbalizations, and diagrams. However, we did not give a formal semantics then.The purpose of this paper is to add a clear, formal and purely declarative semantics to the proposed ORM-transactions. The paper also formally defines rollbacks and illustrates everything with examples (including a solution to a well-known transaction specification problem). The extension of ORM with an expressive set of completely declaratively specified transactions makes ORM complete as a database specification method at the conceptual level.     

Satisfiability and containment of recursive SHACL

The Shapes Constraint Language (SHACL) is the recent W3C recommendation language for validating RDF data, by verifying certain shapes on graphs. Previous work has largely focused on the validation problem, while the standard decision problems of satisfiability and containment, crucial for design and optimisation purposes, have only been investigated for simplified versions of SHACL. Moreover, the SHACL specification does not define the semantics of recursively-defined constraints, which led to several alternative recursive semantics being proposed in the literature. The interaction between these different semantics and important decision problems has not been investigated yet. In this article we provide a comprehensive study of the different features of SHACL, by providing a translation to a new first-order language, called SCL, that precisely captures the semantics of SHACL. We also present MSCL, a second-order extension of SCL, which allows us to define, in a single formal logic framework, the main recursive semantics of SHACL. Within this language we also provide an effective treatment of filter constraints which are often neglected in the related literature. Using this logic we provide a detailed map of (un)decidability and complexity results for the satisfiability and containment decision problems for different SHACL fragments. Notably, we prove that both problems are undecidable for the full language, but we present decidable combinations of interesting features, even in the face of recursion.     

Beyond multi-adjoint logic programming

In ‘multi-adjoint logic programming’, MALP in brief, each fuzzy logic program is associated with its own ‘multi-adjoint lattice’ for modelling truth degrees beyond the simpler case of true and false, where a large set of fuzzy connectives can be defined. On this wide repertoire, it is crucial to connect each implication symbol with a proper conjunction thus conforming constructs of the form (←_i, &_i) called ‘adjoint pairs’, whose use directly affects both declarative and operational semantics of the MALP framework. In this work, we firstly show how the strong dependence of adjoint pairs can be largely weakened for an interesting ‘sub-class’ of MALP programs. Then, we reason in a similar way till conceiving a ‘super-class’ of fuzzy logic programs beyond MALP, which definitively drops out the need for using adjoint pairs, since the new semantics behaviour relies on much more relaxed lattices than multi-adjoint ones.     

Vivid: A framework for heterogeneous problem solving

We introduce Vivid, a domain-independent framework for mechanized heterogeneous reasoning that combines diagrammatic and symbolic representation and inference. The framework is presented in the form of a family of denotational proof languages (DPLs). We present novel formal structures, called named system states, that are specifically designed for modeling potentially underdetermined diagrams. These structures allow us to deal with incomplete information, a pervasive feature of heterogeneous problem solving. We introduce a notion of attribute interpretations that enables us to interpret first-order relational signatures into named system states, and develop a formal semantic framework based on 3-valued logic. We extend the assumption-base semantics of DPLs to accommodate diagrammatic reasoning by introducing general inference mechanisms for the valid extraction of information from diagrams, and for the incorporation of sentential information into diagrams. A rigorous big-step operational semantics is given, on the basis of which we prove that the framework is sound. We present examples of particular instances of Vivid in order to solve a series of problems, and discuss related work.     

Agents via Mixed-Mode Computation in Linear Logic

Agent systems based on the Belief, Desire and Intention model of Rao and Georgeff have been used for a number of successful applications. However, it is often difficult to learn how to apply such systems, due to the complexity of both the semantics of the system and the computational model. In addition, there is a gap between the semantics and the concepts that are presented to the programmer. In this paper we address these issues by re-casting the foundations of such systems into a logic programming framework. In particular we show how the integration of backward- and forward-chaining techniques for linear logic provides a natural starting point for this investigation. We discuss how the integrated system provides for the interaction between the proactive and reactive parts of the system, and we discuss several aspects of this interaction. In particular, one perhaps surprising outcome is that goals and plans may be thought of as declarative and procedural aspects of the same concept. We also discuss the language design issues for such a system, and particularly the way in which the potential choices for rule evaluation in a forward-chaining manner is crucial to the behaviour of the system.     

Autoepistemic logics as a unifying framework for the semantics of logic programs

In this paper, it is shown that a three-valued autoepistemic logic provides an elegant unifying framework for some of the major semantics of normal and disjunctive logic programs and logic programs with classical negation, namely, the stable semantics, the well-founded semantics, supported models, Fitting's semantics, Kunen's semantics, the stationary semantics, and answer sets. For the first time, so many semantics are embedded into one logic. The framework extends previous results—by Gelfond, Lifschitz, Marek, Subrahmanian, and Truszczynski —on the relationships between logic programming and Moore's autoepistemic logic. The framework suggests several new semantics for negation-as-failure. In particular, we will introduce the epistemic semantics for disjunctive logic programs. In order to motivate the epistemic semantics, an interesting class of applications called ignorance tests will be formalized; it will be proved that ignorance tests can be defined by means of the epistemic semantics, but not by means of the old semantics for disjunctive programs. The autoepistemic framework provides a formal foundation for an environment that integrates different forms of negation. The role of classical negation and various forms of negation-by-failure in logic programming will be briefly discussed.     

Exogenous Probabilistic Computation Tree Logic

We define a logic EpCTL for reasoning about the evolution of probabilistic systems. System states correspond to probability distributions over classical states and the system evolution is modelled by probabilistic Kripke structures that capture both stochastic and non–deterministic transitions. The proposed logic is a temporal enrichment of Exogenous Probabilistic Propositional Logic (EPPL). The model-checking problem for EpCTL is analysed and the logic is compared with PCTL; the semantics of the former is defined in terms of probability distributions over sets of propositional symbols, whereas the latter is designed for reasoning about distributions over paths of possible behaviour. The intended application of the logic is as a specification formalism for properties of communication protocols, and security protocols in particular; to demonstrate this, we specify relevant security properties for a classical contract signing protocol and for the so–called quantum one–time pad.     

Static analysis of a parallel logic language based on the blackboard model

Shared Prolog is a parallel logic language based on the blackboard interpretation of logic programming. In such an interpretation a logic program is seen as a set of rules executed by a set of agents cooperating via a shared working memory called the blackboard. A distributed interpreter for Shared Prolog was implemented and described in another paper, where the blackboard was a centralized data structure. In this paper we show how the blackboard can be distributed using some static analysis techniques. The basic idea is to perform an abstract interpretation starting from the Shared Prolog operational semantics to generate data structures which represent possible interactions and links among agents. The resulting data structures are used to reduce the number of run time communication operations in an implementation distributed over a network of workstations.     

Scenario-based and value-based specification mining: better together

Specification mining takes execution traces as input and extracts likely program invariants, which can be used for comprehension, verification, and evolution related tasks. In this work we integrate scenario-based specification mining, which uses a data-mining algorithm to suggest ordering constraints in the form of live sequence charts, an inter-object, visual, modal, scenario-based specification language, with mining of value-based invariants, which detects likely invariants holding at specific program points. The key to the integration is a technique we call scenario-based slicing, running on top of the mining algorithms to distinguish the scenario-specific invariants from the general ones. The resulting suggested specifications are rich, consisting of modal scenarios annotated with scenario-specific value-based invariants, referring to event parameters and participating object properties. We have implemented the mining algorithm and the visual presentation of the mined scenarios within a standard development environment. An evaluation of our work over a number of case studies shows promising results in extracting expressive specifications from real programs, which could not be extracted previously. The more expressive the mined specifications, the higher their potential to support program comprehension and testing.     

L-wrappers: concepts,properties and construction

In this paper, we propose a novel class of wrappers (logic wrappers) inspired by the logic prog- ramming paradigm. The developed Logic wrappers (L-wrapper) have declarative semantics, and therefore: (i) their specification is decoupled from their implementation and (ii) they can be generated using inductive logic programming. We also define a convenient way for mapping L-wrappers to XSLT for efficient processing using available XSLT processing engines.