EMTPL and its relation to first order logic

Time and change are notions that seems unavoidable in some areas of work and investigation, languages that can deal with these notions are necessary. At the same time, methods for a proper time handling are quite complex, mainly because problem’s complexity and variety of solutions. Between the languages developed to cover these expectations, under a specific view of time, are [Cobo and Augusto, 1999a] EMTLP and a metric temporal logic’s fragment, bounded universal Horn formulae analyzed by Brzoska [Brzoska, 1998]. Although both of them performed metric temporal programming, they face this fact from different perspectives. In this work we are going to try a comparison between them after a short overview over each. In this first stage we present a way of representing EMTPL’s in first order logic using Brzoska’s approximation as a bridge, and we also compare some aspects of both programming languages.Eje: I - Workshop de Ingeniería de Software y Base de DatosRed de Universidades con Carreras en Informática (RedUNCI

A Flexible and Efficient Temporal Logic Tool for Python: PyTeLo

Temporal logic is an important tool for specifying complex behaviors of systems. It can be used to define properties for verification and monitoring, as well as goals for synthesis tools, allowing users to specify rich missions and tasks. Some of the most popular temporal logics include Metric Temporal Logic (MTL), Signal Temporal Logic (STL), and weighted STL (wSTL), which also allow the definition of timing constraints. In this work, we introduce PyTeLo, a modular and versatile Python-based software that facilitates working with temporal logic languages, specifically MTL, STL, and wSTL. Applying PyTeLo requires only a string representation of the temporal logic specification and, optionally, the dynamics of the system of interest. Next, PyTeLo reads the specification using an ANTLR-generated parser and generates an Abstract Syntax Tree (AST) that captures the structure of the formula. For synthesis, the AST serves to recursively encode the specification into a Mixed Integer Linear Program (MILP) that is solved using a commercial solver such as Gurobi. We describe the architecture and capabilities of PyTeLo and provide example applications highlighting its adaptability and extensibility for various research problems

EMTPL and its relation to first order logic

Time and change are notions that seems unavoidable in some areas of work and investigation, languages that can deal with these notions are necessary. At the same time, methods for a proper time handling are quite complex, mainly because problem’s complexity and variety of solutions. Between the languages developed to cover these expectations, under a specific view of time, are [Cobo and Augusto, 1999a] EMTLP and a metric temporal logic’s fragment, bounded universal Horn formulae analyzed by Brzoska [Brzoska, 1998]. Although both of them performed metric temporal programming, they face this fact from different perspectives. In this work we are going to try a comparison between them after a short overview over each. In this first stage we present a way of representing EMTPL’s in first order logic using Brzoska’s approximation as a bridge, and we also compare some aspects of both programming languages.Eje: I - Workshop de Ingeniería de Software y Base de DatosRed de Universidades con Carreras en Informática (RedUNCI

The Stable Model Semantics of Datalog with Metric Temporal Operators

We introduce negation under the stable model semantics in DatalogMTL - a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rational timeline, and decidable in EXPSPACE in data complexity over the integer timeline. We also show that, if we restrict our attention to forward-propagating programs, reasoning over the integer timeline becomes PSPACE-complete in data complexity, and hence, no harder than over positive programs; however, reasoning over the rational timeline in this fragment remains undecidable. Under consideration in Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming (TPLP

The stable model semantics of datalog with metric temporal operators

We introduce negation under the stable model semantics in DatalogMTL - a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the temporal dimension provided by metric operators. We show that, in this setting, reasoning becomes undecidable over the rational timeline, and decidable in EXPSPACE in data complexity over the integer timeline. We also show that, if we restrict our attention to forward-propagating programs, reasoning over the integer timeline becomes PSPACE-complete in data complexity, and hence, no harder than over positive programs; however, reasoning over the rational timeline in this fragment remains undecidable. Under consideration in Theory and Practice of Logic Programming (TPLP)

Temporal reasoning in a logic programming language with modularity

Actualmente os Sistemas de Informação Organizacionais (SIO) lidam cada vez mais com informação que tem dependências temporais. Neste trabalho concebemos um ambiente de trabalho para construir e manter SIO Temporais. Este ambiente assenta sobre um linguagem lógica denominada Temporal Contextua) Logic Programming que integra modularidade com raciocínio temporal fazendo com que a utilização de um módulo dependa do tempo do contexto. Esta linguagem é a evolução de uma outra, também introduzida nesta tese, que combina Contextua) Logic Programming com Temporal Annotated Constraint Logic Programming, na qual a modularidade e o tempo são características ortogonais. Ambas as linguagens são formalmente discutidas e exemplificadas. As principais contribuições do trabalho descrito nesta tese incluem: • Optimização de Contextua) Logic Programming (CxLP) através de interpretação abstracta. • Sintaxe e semântica operacional para uma linguagem que combina de um modo independente as linguagens Temporal Annotated Constraint Logic Programming (TACLP) e CxLP. É apresentado um compilador para esta linguagem. • Linguagem (sintaxe e semântica) que integra de um modo inovador modularidade (CxLP) com raciocínio temporal (TACLP). Nesta linguagem a utilização de um dado módulo está dependente do tempo do contexto. É descrito um interpretador e um compilador para esta linguagem. • Ambiente de trabalho para construir e fazer a manutenção de SIO Temporais. Assenta sobre uma especificação revista da linguagem ISCO, adicionando classes e manipulação de dados temporais. É fornecido um compilador em que a linguagem resultante é a descrita no item anterior. ABSTRACT- Current Organisational Information Systems (OIS) deal with more and more Infor-mation that, is time dependent. In this work we provide a framework to construct and maintain Temporal OIS. This framework builds upon a logical language called Temporal Contextual. Logic Programming that deeply integrates modularity with tem-poral reasoning making the usage of a module time dependent. This language is an evolution of another one, also introduced in this thesis, that combines Contextual Logic Programming with Temporal Annotated Constraint Logic Programming where modularity and time are orthogonal features. Both languages are formally discussed and illustrated. The main contributions of the work described in this thesis include: • Optimisation of Contextual Logic Programming (CxLP) through abstract interpretation. • Syntax and operational semantics for an independent combination of the temporal framework Temporal Annotated Constraint Logic Programming (TACLP) and CxLP. A compiler for this language is also provided. • Language (syntax and semantics) that integrates in a innovative way modularity (CxLP) with temporal reasoning (TACLP). In this language the usage of a given module depends of the time of the context. An interpreter and a compiler for this language are described. • Framework to construct and maintain Temporal Organisational Information Systems. It builds upon a revised specification of the language ISCO, adding temporal classes and temporal data manipulation. A compiler targeting the language presented in the previous item is also given

Run Time verifcation of Hybrid Systems

The growing use of computers in modern control systems has led to the develop- ment of complex dynamic systems known as hybrid systems, which integrates both discrete and continuous systems. Given that hybrid systems are systems that operates in real time allowing for changes in continuous state over time periods, and discrete state changes across zero time, their modelling, analysis and verification becomes very difficult. The formal verifications of such systems based on specifications that can guar- antee their behaviour is very important especially as it pertains to safety critical applications. Accordingly, addressing such verifications issues are important and is the focus of this thesis. In this thesis, in order to actualise the specification and verification of hybrid systems, Interval Temporal Logic(ITL) was adopted as the underlying formalism given its inherent characteristics of providing methods that are flexible for both propositional and first-order reasoning regarding periods found in hardware and software system’s descriptions. Given that an interval specifies the behaviour of a system, specifications of such systems are therefore represented as a set of intervals that can be used to gain an understanding of the possible behaviour of the system in terms of its composition whether in sequential or parallel form. ITL is a powerful tool that can handle both forms of composition given that it offers very strong and extensive proof and specifi- cation techniques to decipher essential system properties including safety, liveliness and time projections.However, a limitation of ITL is that the intervals within its framework are considered to be a sequence of discrete states. Against this back- drop, the current research provides an extension to ITL with the view to deal with verification and other related issues that centres around hybrid systems. The novelty within this new proposition is new logic termed SPLINE Interval Temporal Logic (SPITL) in which not only a discrete behaviour can be expressed, but also a continuous behaviour can be represented in the form of a spline i.e. the interval is considered to be a sequence of continuous phases instead of a sequence of discrete states. The syntax and semantics of the newly developed SPITL are provided in this thesis and the new extension of the interval temporal logic using a hybrid system as a case study. The overall framework adopted for the overall struc- ture of SPITL is based on three fundamental steps namely the formal specification of hybrid systems is expressed in SPLINE Interval Temporal Logic, followed by the executable subset of ITL, called Tempura, which is used to develop and test a hybrid system specification that is written in SPITL and finally a runtime verification tool for ITL called AnaTempura which is linked with Matlab in order to use them as an integrated tool for the verification of hybrid systems specification. Overall, the current work contributes to the growing body of knowledge in hybrid systems based on the following three major milestones namely: i. the proposition of a new logic termed SPITL; ii. executable subset, Tempura, integrated with SPITL specification for hybrid systems; and iii. the development of a tool termed Ana Tempura which is integrated with Matlab to ensure accurate runtime verification of results

Invariant-free deduction systems for temporal logic

In this thesis we propose a new approach to deduction methods for temporal logic. Our proposal is based on an inductive definition of eventualities that is different from the usual one. On the basis of this non-customary inductive definition for eventualities, we first provide dual systems of tableaux and sequents for Propositional Linear-time Temporal Logic (PLTL). Then, we adapt the deductive approach introduced by means of these dual tableau and sequent systems to the resolution framework and we present a clausal temporal resolution method for PLTL. Finally, we make use of this new clausal temporal resolution method for establishing logical foundations for declarative temporal logic programming languages. The key element in the deduction systems for temporal logic is to deal with eventualities and hidden invariants that may prevent the fulfillment of eventualities. Different ways of addressing this issue can be found in the works on deduction systems for temporal logic. Traditional tableau systems for temporal logic generate an auxiliary graph in a first pass.Then, in a second pass, unsatisfiable nodes are pruned. In particular, the second pass must check whether the eventualities are fulfilled. The one-pass tableau calculus introduced by S. Schwendimann requires an additional handling of information in order to detect cyclic branches that contain unfulfilled eventualities. Regarding traditional sequent calculi for temporal logic, the issue of eventualities and hidden invariants is tackled by making use of a kind of inference rules (mainly, invariant-based rules or infinitary rules) that complicates their automation. A remarkable consequence of using either a two-pass approach based on auxiliary graphs or aone-pass approach that requires an additional handling of information in the tableau framework, and either invariant-based rules or infinitary rules in the sequent framework, is that temporal logic fails to carry out the classical correspondence between tableaux and sequents. In this thesis, we first provide a one-pass tableau method TTM that instead of a graph obtains a cyclic tree to decide whether a set of PLTL-formulas is satisfiable. In TTM tableaux are classical-like. For unsatisfiable sets of formulas, TTM produces tableaux whose leaves contain a formula and its negation. In the case of satisfiable sets of formulas, TTM builds tableaux where each fully expanded open branch characterizes a collection of models for the set of formulas in the root. The tableau method TTM is complete and yields a decision procedure for PLTL. This tableau method is directly associated to a one-sided sequent calculus called TTC. Since TTM is free from all the structural rules that hinder the mechanization of deduction, e.g. weakening and contraction, then the resulting sequent calculus TTC is also free from this kind of structural rules. In particular, TTC is free of any kind of cut, including invariant-based cut. From the deduction system TTC, we obtain a two-sided sequent calculus GTC that preserves all these good freeness properties and is finitary, sound and complete for PLTL. Therefore, we show that the classical correspondence between tableaux and sequent calculi can be extended to temporal logic. The most fruitful approach in the literature on resolution methods for temporal logic, which was started with the seminal paper of M. Fisher, deals with PLTL and requires to generate invariants for performing resolution on eventualities. In this thesis, we present a new approach to resolution for PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Our method is based on the dual methods of tableaux and sequents for PLTL mentioned above. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called TRS-resolution, that extends classical propositional resolution. Finally, we prove that TRS-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTL. In the field of temporal logic programming, the declarative proposals that provide a completeness result do not allow eventualities, whereas the proposals that follow the imperative future approach either restrict the use of eventualities or deal with them by calculating an upper bound based on the small model property for PLTL. In the latter, when the length of a derivation reaches the upper bound, the derivation is given up and backtracking is used to try another possible derivation. In this thesis we present a declarative propositional temporal logic programming language, called TeDiLog, that is a combination of the temporal and disjunctive paradigms in Logic Programming. We establish the logical foundations of our proposal by formally defining operational and logical semantics for TeDiLog and by proving their equivalence. Since TeDiLog is, syntactically, a sublanguage of PLTL, the logical semantics of TeDiLog is supported by PLTL logical consequence. The operational semantics of TeDiLog is based on TRS-resolution. TeDiLog allows both eventualities and always-formulas to occur in clause heads and also in clause bodies. To the best of our knowledge, TeDiLog is the first declarative temporal logic programming language that achieves this high degree of expressiveness. Since the tableau method presented in this thesis is able to detect that the fulfillment of an eventuality is prevented by a hidden invariant without checking for it by means of an extra process, since our finitary sequent calculi do not include invariant-based rules and since our resolution method dispenses with invariant generation, we say that our deduction methods are invariant-free.CYCIT (ref. TIC98-0949-C02-02), CYCIT (ref. TIC2001-2476-C03-03), CYCIT (ref. TIN2004-07925-C03-03), CICYT (ref. TIN2007-66523), University of the Basque Country (ref. UPV-EHU GIU07/35), University of the Basque Country (ref. UFI11/45

Programming in metric temporal logic

AbstractWe present a fragment of metric temporal logic called bounded universal Horn formulae as a theoretical basis for temporal reasoning in logic programming. We characterize its semantics in terms of fixed points and canonical models, and present an efficient proof method as operational semantics based on SLD-resolution with constraints. Although the complexity of real-time logics is very high in general — the validity problem for most of them is Π1l-complete already for propositional fragments in case of dense time structures — we show that the class of bounded universal Horn formulae admits complete and efficient proof methods exploiting uniform proofs and linear time complexity of basic steps of the proof method. The results obtained heavily rely on the fragment investigated and make it necessary to establish some basic results like compactness and approximation of the least model by at most ω-steps of the corresponding fixed point operator directly without recourse to standard methods (in dense case). The fragment itself is sufficiently expressive for a variety of applications ranging from real-time systems, temporal (deductive) data bases, and sequence evaluation purposes. We show that the fragment is the greatest of the metric temporal logic — in discrete and dense case — having the properties classically desired for logic programming languages