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A strongly complete logic of dense time intervals
 Proceedings of the Workshop on Logics for Resource Bounded Agents, Malaga
, 2006
"... michal,bezem¡ We discuss briefly the duality (or rather, complementarity) of system descriptions based on actions and transitions, on the one hand, and states and their changes, on the other. We settle for the latter and present a simple language, for describing state changes, which is parameterized ..."
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michal,bezem¡ We discuss briefly the duality (or rather, complementarity) of system descriptions based on actions and transitions, on the one hand, and states and their changes, on the other. We settle for the latter and present a simple language, for describing state changes, which is parameterized by an arbitrary language for describing properties of the states. The language can be viewed as a simple fragment of step logic, admitting however various extensions by appropriate choices of the underlying logic. Alternatively, it can be seen as a very specific fragment of temporal logic (with a variant of ‘until ’ or ‘chop ’ operator), and is interpreted over dense (possibly continuous) linear time. The reasoning system presented here is sound, as well as strongly complete and decidable (provided that so is the parameter logic for reasoning about a single state). We give the main idea of the completeness proof and suggest a wide range of possible applications (action based descriptions, active logic, bounded agents), which is a simple consequence of the parametric character of both the language and the reasoning system. 1
TwoVariable Logic with Two Order Relations (Extended Abstract)
"... The finite satisfiability problem for twovariable logic over structures with unary relations and two order relations is investigated. Firstly, decidability is shown for structures with one total preorder relation and one linear order relation. More specifically, we show that this problem is comple ..."
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The finite satisfiability problem for twovariable logic over structures with unary relations and two order relations is investigated. Firstly, decidability is shown for structures with one total preorder relation and one linear order relation. More specifically, we show that this problem is complete for EXPSPACE. As a consequence, the same upper bound applies to the case of two linear orders. Secondly, we prove undecidability for structures with two total preorder relations as well as for structures with one total preorder and two linear order relations. Further, we point out connections to other logics. Decidability is shown for twovariable logic on data words with orders on both positions and data values, but without a successor relation. We also study “partial models” of compass and interval temporal logic and prove decidability for some of their fragments.
Quality Checking of Medical Guidelines using Interval Temporal Logics
, 2007
"... Computerbased decision support in healthcare is becoming increasingly important in recent years. Clinical Practise Guidelines (CPGs) are documents supporting healthcare professionals in managing treatment of patients in order to avoid nonstandard practices or outcomes. Following ideas from publ ..."
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Computerbased decision support in healthcare is becoming increasingly important in recent years. Clinical Practise Guidelines (CPGs) are documents supporting healthcare professionals in managing treatment of patients in order to avoid nonstandard practices or outcomes. Following ideas from publications of Hommersom, Lucas, and Balser, here we promote the use of temporal logics in order for formal specification and verification of CPGs. Unlike the works mentioned above, here we advocate the use of intervalbased temporal logics instead of pointbased ones. In particular, we discuss the possibility of applying Propositional Neighborhood Logic (PNL) and a metric extension of it, called MPNL, to CPGs, in order to enable explicitly take into account the duration of medical events and procedures. We argue that PNL alone can subsume the expressiveness achieved by pointbased logics, and that intervalbased temporal logics in general provide much more detailed and precise formalization of CPGs.
Verification of realtime systems: . . .
, 2006
"... We address a number of limitations of Timed Automata and realtime modelcheckers, which undermine the reliability of formal verification. In particular, we focus on the modelchecker Uppaal as a representative of this technology. Timelocks and Zeno runs represent anomalous behaviours in a timed aut ..."
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We address a number of limitations of Timed Automata and realtime modelcheckers, which undermine the reliability of formal verification. In particular, we focus on the modelchecker Uppaal as a representative of this technology. Timelocks and Zeno runs represent anomalous behaviours in a timed automaton, and may invalidate the verification of safety and liveness properties. Currently, modelcheckers do not offer adequate support to prevent or detect such behaviours. In response, we develop new methods to guarantee timelockfreedom and absence of Zeno runs, which improve and complement the existent support. We implement these methods in a tool to check Uppaal specifications. The requirements language of modelcheckers is not well suited to express sequence and iteration of events, or past computations. As a result, validation problems may arise during verification (i.e., the property that we verify may not accurately reflect the intended requirement). We study the logic PITL, a rich propositional subset of Interval Temporal Logic, where these requirements can be more intuitively expressed than in modelcheckers. However, PITL has a decision procedure with a worstcase nonelementary complexity, which has hampered the
Proceedings of the Workshop on Logics for ResourceBounded Agents
"... Logics of knowledge and belief, as well as other attitudes such as desire or intention, have been extensively studied. However, most of the treatments of knowledge and belief make strong and idealised assumptions about the reasoners. For example, traditional epistemic logic says that agents know all ..."
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Logics of knowledge and belief, as well as other attitudes such as desire or intention, have been extensively studied. However, most of the treatments of knowledge and belief make strong and idealised assumptions about the reasoners. For example, traditional epistemic logic says that agents know all logical consequences of their knowledge. Similarly, logics of action and strategic interaction are usually based on game theoretic models which assume perfect rationality. Models based on such assumptions can be used to describe ideal agents without bounds on resources such as time, memory, etc, but they fail to accurately describe nonideal agents which are computationally bounded. The Workshop on Logics for ResourceBounded Agents was held as a part of the 18th European Summer School in Logic, Language and Information (ESSLLI, Malaga, 2006), in order to provide a forum for advanced PhD students and researchers to present and discuss possible solutions to the problem of formally capturing the properties of knowledge, belief, action, etc., of nonidealised resourcebounded agents with colleagues and researchers who work in logic, computer
Decidability of the Logics of the Reflexive Subinterval and Superinterval Relations over Finite Linear Orders
"... Abstract—An interval temporal logic is a propositional, multimodal logic interpreted over interval structures of partial orders. The semantics of each modal operator are given in the standard way with respect to one of the natural accessibility relations defined on such interval structures. In this ..."
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Abstract—An interval temporal logic is a propositional, multimodal logic interpreted over interval structures of partial orders. The semantics of each modal operator are given in the standard way with respect to one of the natural accessibility relations defined on such interval structures. In this paper, we consider the modal operators based on the (reflexive) subinterval relation and the (reflexive) superinterval relation. We show that the satisfiability problems for the interval temporal logics featuring either or both of these modalities, interpreted over interval structures of finite linear orders, are all PSPACEcomplete. These results fill a gap in the known complexity results for interval temporal logics. Keywordsinterval temporal logic; decidability; computational complexity I.
HyLMoC A Model Checker for Hybrid Logic
"... Abstract. The current technological trend depicts a scenario in which space, and more generally the environment in which the computation takes place, represents a key aspect that must be considered in order to improve systems context awareness. Reasoning about such context can be interpreted as spat ..."
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Abstract. The current technological trend depicts a scenario in which space, and more generally the environment in which the computation takes place, represents a key aspect that must be considered in order to improve systems context awareness. Reasoning about such context can be interpreted as spatial reasoning, which means not only to be able to carry out inferences about the space itself, but also inferences about spatially related information according a given background knowledge. Past works have shown that hybrid modal logics are a powerful and rich formalism to model qualitative spatial reasoning and reasoning on information spread into graphlike structures. In this paper we present the preliminary results we obtained in designing and implementing HyLMoC, a model checking system for hybrid modal logics. The functionalities of the model checker are based on backend module that accepts as inputs a list of hybrid modal formulas and the specification of a labeled graph structure that is compliant with the characteristics of a Kripke model. The current implementation of the backend allows to perform different reasoning tasks with respect to those inputs: Local and Global model checking, and Allworlds model checking. 1
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"... Undecidability and temporal logic: some landmarks from Turing to the present (Extended abstract) ..."
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Undecidability and temporal logic: some landmarks from Turing to the present (Extended abstract)
Bounded Modelchecking of Discrete Duration Calculus ∗
"... Fränzle and Hansen investigated the modelchecking problem of the subset of Duration Calculus without individual variables and quantifications w.r.t. some approximation semantics by reduction to the decision problem of Presburger Arithmetic, thus obtained a modelchecking algorithm with 4fold expon ..."
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Fränzle and Hansen investigated the modelchecking problem of the subset of Duration Calculus without individual variables and quantifications w.r.t. some approximation semantics by reduction to the decision problem of Presburger Arithmetic, thus obtained a modelchecking algorithm with 4fold exponential complexity [6, 7]. As an alternative, inspired by their work, we consider the bounded modelchecking problem of the subset in the context of the standard discretetime semantics in this paper. Based on our previous work [20], we reduce this problem to the reachability problem of timed automata. The complexity of our approach is singly exponential in the size of formulas and quadratic in the number of states of models. We implement our approach using UPPAAL and demonstrate its efficiency by some examples.