Local Distributed Model Checking of Reg CTL

AbstractThe paper is devoted to the problem of extending the temporal logic CTL so that it is more expressive and complicated properties can be expressed more succinctly. The specification language Reg CTL, an extension of CTL, is proposed. In Reg CTL every CTL temporal operator is augmented with a regular expression restricting thus moments when the validity is required. The resulting logic is more expressive than previous extensions of CTL with regular expressions. Reg CTL can be model-checked on-the-fly and the model checking algorithm is well distributable

Efficient Large-scale Trace Checking Using MapReduce

The problem of checking a logged event trace against a temporal logic specification arises in many practical cases. Unfortunately, known algorithms for an expressive logic like MTL (Metric Temporal Logic) do not scale with respect to two crucial dimensions: the length of the trace and the size of the time interval for which logged events must be buffered to check satisfaction of the specification. The former issue can be addressed by distributed and parallel trace checking algorithms that can take advantage of modern cloud computing and programming frameworks like MapReduce. Still, the latter issue remains open with current state-of-the-art approaches. In this paper we address this memory scalability issue by proposing a new semantics for MTL, called lazy semantics. This semantics can evaluate temporal formulae and boolean combinations of temporal-only formulae at any arbitrary time instant. We prove that lazy semantics is more expressive than standard point-based semantics and that it can be used as a basis for a correct parametric decomposition of any MTL formula into an equivalent one with smaller, bounded time intervals. We use lazy semantics to extend our previous distributed trace checking algorithm for MTL. We evaluate the proposed algorithm in terms of memory scalability and time/memory tradeoffs.Comment: 13 pages, 8 figure

Complexity of ITL model checking: some well-behaved fragments of the interval logic HS

Model checking has been successfully used in many computer science fields, including artificial intelligence, theoretical computer science, and databases. Most of the proposed solutions make use of classical, point-based temporal logics, while little work has been done in the interval temporal logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shoham's modal logic of time intervals HS over finite Kripke structures (under the homogeneity assumption) and an EXPSPACE model checking procedure for two meaningful fragments of it have been proposed. In this paper, we show that more efficient model checking procedures can be developed for some expressive enough fragments of HS

A complete reified temporal logic and its applications

Temporal representation and reasoning plays a fundamental and increasingly important role in some areas of Computer Science and Artificial Intelligence. A natural approach to represent and reason about time-dependent knowledge is to associate them with instantaneous time points and/or durative time intervals. In particular, there are various ways to use logic formalisms for temporal knowledge representation and reasoning. Based on the chosen logic frameworks, temporal theories can be classified into modal logic approaches (including prepositional modal logic approaches and hybrid logic approaches) and predicate logic approaches (including temporal argument methods and temporal reification methods). Generally speaking, the predicate logic approaches are more expressive than the modal logic approaches and among predicate logic approaches, temporal reification methods are even more expressive for representing and reasoning about general temporal knowledge. However, the current reified temporal logics are so complicate that each of them either do not have a clear definition of its syntax and semantics or do not have a sound and complete axiomatization. In this thesis, a new complete reified temporal logic (CRTL) is introduced which has a clear syntax, semantics, and a complete axiomatic system by inheriting from the initial first order language. This is the main improvement made to the reification approaches for temporal representation and reasoning. It is a true reified logic since some meta-predicates are formally defined that allow one to predicate and quantify over prepositional terms, and therefore provides the expressive power to represent and reason about both temporal and non-temporal relationships between prepositional terms. For a special case, the temporal model of the simplified CRTL system (SCRTL) is defined as scenarios and graphically represented in terms of a directed, partially weighted or attributed, simple graph. Therefore, the problem of matching temporal scenarios is transformed into conventional graph matching. For the scenario graph matching problem, the traditional eigen-decomposition graph matching algorithm and the symmetric polynomial transform graph matching algorithm are critically examined and improved as two new algorithms named meta-basis graph matching algorithm and sort based graph matching algorithm respectively, where the meta-basis graph matching algorithm works better for 0-1 matrices while the sort based graph matching algorithm is more suitable for continuous real matrices. Another important contribution is the node similarity graph matching framework proposed in this thesis, based on which the node similarity graph matching algorithms can be defined, analyzed and extended uniformly. We prove that that all these node similarity graph matching algorithms fail to work for matching circles

A framework for qualitative reasoning about solid objects

Predicting the behavior of a qualitatively described system of solid objects requires a combination of geometrical, temporal, and physical reasoning. Methods based upon formulating and solving differential equations are not adequate for robust prediction, since the behavior of a system over extended time may be much simpler than its behavior over local time. A first-order logic, in which one can state simple physical problems and derive their solution deductively, without recourse to solving the differential equations, is discussed. This logic is substantially more expressive and powerful than any previous AI representational system in this domain

A Tableau Calculus for Temporal Description Logic: The Constant Domain Case.

We show how to combine the standard tableau system for the basic description logic ALC and Wolper´s tableau calculus for propositional temporal logic PTL (with the temporal operators ‘next-time’ and ‘until’) in order to design a terminating sound and complete tableau-based satisfiability-checking algorithm for the temporal description logic PTL ALC of [19] interpreted in models with constant domains. We use the method of quasimodels [17, 15] to represent models with infinite domains, and the technique of minimal types [11] to maintain these domains constant. The combination is flexible and can be extended to more expressive description logics or even do decidable fragments of first-order temporal logics

Model Checking of RegCTL

The paper is devoted to the problem of extending the temporal logic CTL so that it is more expressive and complicated properties can be expressed in a more readable form. The specification language RegCTL, an extension of CTL, is proposed. In RegCTL every CTL temporal operator is augmented with a regular expression, thus restricting moments when the validity is required. We propose a local distributed model checking algorithm for RegCTL

Visibly Linear Dynamic Logic

We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a variable to its original value after its execution, even in the presence of an unbounded number of intermediate recursive calls. We prove that VLDL describes exactly the $\omega$-visibly pushdown languages. Thus it is strictly more expressive than LTL and able to express recursive properties of programs with unbounded call stacks. The main technical contribution of this work is a translation of VLDL into $\omega$-visibly pushdown automata of exponential size via one-way alternating jumping automata. This translation yields exponential-time algorithms for satisfiability, validity, and model checking. We also show that visibly pushdown games with VLDL winning conditions are solvable in triply-exponential time. We prove all these problems to be complete for their respective complexity classes.Comment: 25 Page