Implicates and Reduction Techniques for Temporal Logics (original) (raw)

Simplifying Inductive Schemes in Temporal Logic

2019

In propositional temporal logic, the combination of the connectives “tomorrow” and “always in the future” require the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula. 2012 ACM Subject Classification Theory of computation → Modal and temporal logics

Implementing Temporal Logics: Tools for Execution and Proof (Tutorial Paper)

In this article I will present an overview of a selection of tools for execution and proof based on temporal logic, and outline both the general techniques used and problems encountered in implementing them. This selection is quite subjective, mainly concerning work that has involved researchers I have collaborated with at Liverpool (and, previously, Manchester). The tools considered will mainly be theorem-provers and (logic-based) agent programming languages

Implementing Temporal Logics: Tools for Execution and Proof

2006

In this article I will present an overview of a selection of tools for execution and proof based on temporal logic, and outline both the general techniques used and problems en-countered in implementing them. This selection is quite subjective, mainly concerning work that has involved researchers I have collaborated with at Liverpool (and, previ-ously, Manchester). The tools considered will mainly be theorem-provers and (logic-based) agent programming languages. Specifically:

From Linear Temporal Logic Properties to Rewrite Propositions

Lecture Notes in Computer Science, 2012

In the regular model-checking framework, reachability analysis can be guided by temporal logic properties, for instance to achieve the counter example guided abstraction refinement (CEGAR) objectives. A way to perform this analysis is to translate a temporal logic formula expressed on maximal rewriting words into a "rewrite proposition" -a propositional formula whose atoms are language comparisons, and then to generate semidecision procedures based on (approximations of) the rewrite proposition. This approach has recently been studied using a non-automatic translation method. The extent to which such a translation can be systematised needs to be investigated, as well as the applicability of approximated methods wherever no exact translation can be effected. This paper presents contributions to that effect: (1) we investigate suitable semantics for LTL on maximal rewriting words and their influence on the feasibility of a translation, and (2) we propose a general scheme providing exact results on a fragment of LTL corresponding mainly to safety formulae, and approximations on a larger fragment.

Boolean abstraction for temporal logic satisfiability

2007

Increasing interest towards property based design calls for effective satisfiability procedures for expressive temporal logics, e.g. the IEEE standard Property Specification Language (PSL). In this paper, we propose a new approach to the satisfiability of PSL formulae; we follow recent approaches to decision procedures for Satisfiability Modulo Theory, typically applied to fragments of First Order Logic. The underlying intuition is to combine two interacting search mechanisms: on one side, we search for assignments that satisfy the Boolean abstraction of the problem; on the other, we invoke a solver for temporal satisfiability on the conjunction of temporal formulae corresponding to the assignment. Within this framework, we explore two directions. First, given the fixed polarity of each constraint in the theory solver, aggressive simplifications can be applied. Second, we analyze the idea of conflict reconstruction: whenever a satisfying assignment at the level of the Boolean abstraction results in a temporally unsatisfiable problem, we identify inconsistent subsets that can be used to rule out possibly many other assignments. We propose two methods to extract conflict sets on conjunctions of temporal formulae (one based on BDD-based Model Checking, and one based on SAT-based Simple Bounded Model Checking). We analyze the limits and the merits of the approach with a thorough experimental evaluation. a counterexample trace: the user is working at the level of requirements, and thus the inconsistency should be identified at the same level, e.g. as a subset of inconsistent requirements. Furthermore, this approach may have some limitations: in fact, techniques and tools for temporal logic model checking are focusing on complexity in the model, and even reductions on the temporal logic formula [ST03] are oriented to dominating the complexity in the model.

First-Order Temporal Verification in Practice

Journal of Automated Reasoning, 2005

First-order temporal logic, the extension of first-order logic with operators dealing with time, is a powerful and expressive formalism with many potential applications. This expressive logic can be viewed as a framework in which to investigate problems specified in other logics. The monodic fragment of first-order temporal logic is a useful fragment that possesses good computational properties such as completeness and sometimes even decidability. Temporal logics of knowledge are useful for dealing with situations where the knowledge of agents in a system is involved. In this paper we present a translation from temporal logics of knowledge into the monodic fragment of first-order temporal logic. We can then use a theorem prover for monodic first-order temporal logic to prove properties of the translated formulas. This allows problems specified in temporal logics of knowledge to be verified automatically without needing a specialized theorem prover for temporal logics of knowledge. We present the translation, its correctness, and examples of its use.

Final report:‘Analysis and Mechanisation of Decidable First-Order Temporal Logics’

First-order temporal logic (FOTL) has long been regarded by many as a perfect formalism for program specification and verification, temporal databases, synthesis of programs, model checking, temporal knowledge representation and reasoning, etc. The fatal problem was that mechanisation seemed out of the question, because only 'negative' results (undecidability, non-recursive enumerability) were known. The starting point of this project was the discovery in [HWZ00] of decidable and yet rather expressive 'monodic' fragments of FOTL, which opened new and exciting opportunities for using FOTL in various areas of computer science and artificial intelligence.

Timed Context-Free Temporal Logics

Electronic Proceedings in Theoretical Computer Science, 2018

The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and context-free properties by ensuring decidability and tractability in the combined setting. To this end we introduce two real-time linear temporal logics for specifying quantitative timing context-free requirements in a pointwise semantics setting: Event-Clock Nested Temporal Logic (EC NTL) and Nested Metric Temporal Logic (NMTL). The logic EC NTL is an extension of both the logic CaRet (a context-free extension of standard LTL) and Event-Clock Temporal Logic (a tractable real-time logical framework related to the class of Event-Clock automata). We prove that satisfiability of EC NTL and visibly model-checking of Visibly Pushdown Timed Automata (VPTA) against EC NTL are decidable and EXPTIME-complete. The other proposed logic NMTL is a context-free extension of standard Metric Temporal Logic (MTL). It is well known that satisfiability of future MTL is undecidable when interpreted over infinite timed words but decidable over finite timed words. On the other hand, we show that by augmenting future MTL with future context-free temporal operators, the satisfiability problem turns out to be undecidable also for finite timed words. On the positive side, we devise a meaningful and decidable fragment of the logic NMTL which is expressively equivalent to EC NTL and for which satisfiability and visibly model-checking of VPTA are EXPTIME-complete. * The work by Adriano Peron and Aniello Murano has been partially supported by the GNCS project Formal methods for verification and synthesis of discrete and hybrid systems and by Dept. project MODAL MOdel-Driven Analysis of Critical Industrial Systems.

Simple on-the-fly automatic verification of linear temporal logic

… Testing and Verification, 1995

We present a tableau-based algorithm for obtaining an automaton from a temporal logic formula. The algorithm is geared towards being used in model checking in an "on-the-fly" fashion, that is the automaton can be constructed simultaneously with, and guided by, the generation of the model. In particular, it is possible to detect that a property does not hold by only constructing part of the model and of the automaton. The algorithm can also be used to check the validity of a temporal logic assertion. Although the general problem is PSPACE-complete, experiments show that our algorithm performs quite well on the temporal formulas typically encountered in verification. While basing linear-time temporal logic model-checking upon a transformation to automata is not new, the details of how to do this efficiently, and in "on-the-fly" fashion have never been given.

Annotation-based deduction in temporal logic

Lecture Notes in Computer Science, 1994

This paper presents a deductive system for predicate temporal logic with induction. Representing temporal operators by rst-order expressions enables temporal deduction to use the already developed techniques of rst-order deduction. But when translating from temporal logic to rst-order logic is done indiscriminately, the ensuing quanti cations and comparisons of time expressions encumber formulas, hindering deduction. So in the deductive system presented here, translation occurs more carefully, via rei cation rules. These rules paraphrase selected temporal formulas as nontemporal rst-order formulas with time annotations. This time reication process suppresses quanti cations (the process is analogous to quanti er skolemization) and uses addition instead of complicated combinations of comparisons. Some ordering conditions on arithmetic expressions can arise, but such are handled automatically by a specialpurpose uni cation algorithm plus a decision procedure for Presburger arithmetic. This deductive system is relatively complete. Contents