Parity-energy ATL for Qualitative and Quantitative Reasoning in MAS

In this paper, we introduce a new logic suitable to reason about strategic abilities of multi-agent systems where (teams of) agents are subject to qualitative (parity) and quantitative (energy) constraints and where goals are represented, as usual, by means of temporal properties. We formally define such a logic, named parity-energy-atl (peatl, for short), and we study its model checking problem, which we prove to be decidable with different complexity upper bounds, depending on different choices for the energy range

Alternating (In)Dependence-Friendly Logic

Hintikka and Sandu originally proposed Independence Friendly Logic ([Formula presented]) as a first-order logic of imperfect information to describe game-theoretic phenomena underlying the semantics of natural language. The logic allows for expressing independence constraints among quantified variables, in a similar vein to Henkin quantifiers, and has a nice game-theoretic semantics in terms of imperfect information games. However, the [Formula presented] semantics exhibits some limitations, at least from a purely logical perspective. It treats the players asymmetrically, considering only one of the two players as having imperfect information when evaluating truth, resp., falsity, of a sentence. In addition, truth and falsity of sentences coincide with the existence of a uniform winning strategy for one of the two players in the semantic imperfect information game. As a consequence, [Formula presented] does admit undetermined sentences, which are neither true nor false, thus failing the law of excluded middle. These idiosyncrasies limit its expressive power to the existential fragment of Second Order Logic ([Formula presented]). In this paper, we investigate an extension of [Formula presented], called Alternating Dependence/Independence Friendly Logic ([Formula presented]), tailored to overcome these limitations. To this end, we introduce a novel compositional semantics, generalising the one based on trumps proposed by Hodges for [Formula presented]. The new semantics (i) allows for meaningfully restricting both players at the same time, (ii) enjoys the property of game-theoretic determinacy, (iii) recovers the law of excluded middle for sentences, and (iv) grants [Formula presented] the full descriptive power of [Formula presented]. We also provide an equivalent Herbrand-Skolem semantics and a game-theoretic semantics for the prenex fragment of [Formula presented], the latter being defined in terms of a determined infinite-duration game that precisely captures the other two semantics on finite structures

The optical appearance of a nonsingular de Sitter core black hole geometry under several thin disk emissions

We consider the optical appearance under a thin accretion disk of a regular black hole with a central de Sitter core implementing $\mathcal{O}(l^2/r^2)$ far-corrections to the Schwarzschild black hole. We use the choice $l=0.25M$, which satisfies recently found constraints from the motion of the S2 star around Sgr A$^*$ in this model, and which leads to thermodynamically stable black holes. As the emission model, we suitably adapt ten samples of the Standard Unbound emission profile for a monochromatic intensity in the disk's frame, which have been previously employed in the literature within the context of reproducing General Relativistic Magneto-Hydrodynamic simulations of the accretion flow. We find the usual central brightness depression surrounded by the bright ring cast by the disk's direct emission as well as two non-negligible photon ring contributions. As compared to the usual Schwarzschild solution, the relative luminosities of the latter are significantly boosted, while the size of the former is strongly decreased. We discuss the entanglement of the background geometry and the choice of emission model in generating these black hole images, as well as the capability of these modifications of Schwarzschild solution to pass present and future tests based on their optical appearance when illuminated by an accretion disk.Comment: 12 pages, 5 figure

A novel automata-theoretic approach to timeline-based planning

Timeline-based planning is a well-established approach successfully employed in a number of application domains. A very restricted fragment, featuring only bounded temporal relations and token durations, is expressive enough to capture action-based temporal planning. As for computational complexity, it has been shown to be EXPSPACE-complete when unbounded temporal relations, but only bounded token durations, are allowed. In this paper, we present a novel automata-theoretic characterisation of timeline-based planning where the existence of a plan is shown to be equivalent to the nonemptiness of the language recognised by a nondeterministic finite-state automaton that suitably encodes all the problem constraints (timelines and synchronisation rules). Besides allowing us to restate known complexity results in a fairly natural and compact way, such an alternative characterisation makes it possible to finally establish the exact complexity of the full version of the problem with unbounded temporal relations and token durations, which was still open and turns out to be EXPSPACE-complete. Moreover, the proposed technique is general enough to cope with (infinite) recurrent goals, which received little attention so far, despite being quite common in real-word application scenarios

Decidability and complexity of the fragments of the modal logic of Allen's relations over the rationals

Interval temporal logics provide a natural framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as first-class citizens. Their expressive power and computational behaviour mainly depend on two parameters: the set of modalities they feature and the linear orders over which they are interpreted. In this paper, we consider all fragments of Halpern and Shoham's interval temporal logic hs with a decidable satisfiability problem over the rationals, and we provide a complete classification of them in terms of their expressiveness and computational complexity by solving the last few open problems

Monitors that Learn from Failures: Pairing STL and Genetic Programming

In several domains, systems generate continuous streams of data during their execution, including meaningful telemetry information, that can be used to perform tasks like preemptive failure detection. Deep learning models have been exploited for these tasks with increasing success, but they hardly provide guarantees over their execution, a problem which is exacerbated by their lack of interpretability. In many critical contexts, formal methods, which ensure the correct behaviour of a system, are thus necessary. However, specifying in advance all the relevant properties and building a complete model of the system against which to check them is often out of reach in real-world scenarios. To overcome these limitations, we design a framework that resorts to monitoring, a lightweight runtime verification technique that does not require an explicit model specification, and pairs it with machine learning. Its goal is to automatically derive relevant properties, related to a bad behaviour of the considered system, encoded by means of formulas of Signal Temporal Logic (STL). Results based on experiments performed on well-known benchmark datasets show that the proposed framework is able to effectively anticipate critical system behaviours in an online setting, providing human-interpretable results

Prompt interval temporal logic

Interval temporal logics are expressive formalisms for temporal representation and reasoning, which use time intervals as primitive temporal entities. They have been extensively studied for the past two decades and successfully applied in AI and computer science. Unfortunately, they lack the ability of expressing promptness conditions, as it happens with the commonly-used temporal logics, e.g., LTL: whenever we deal with a liveness request, such as \u201csomething good eventually happens\u201d, there is no way to impose a bound on the delay with which it is fulfilled. In the last years, such an issue has been addressed in automata theory, game theory, and temporal logic. In this paper, we approach it in the interval temporal logic setting. First, we introduce PROMPT-PNL, a prompt extension of the well-studied interval temporal logic PNL, and we prove the undecidability of its satisfiability problem; then, we show how to recover decidability (NEXPTIME-completeness) by imposing a natural syntactic restriction on it

Acta Informatica manuscript No. (will be inserted by the editor) A Complete Classification of the Expressiveness of Interval Logics of Allen’s Relations The General and the Dense Cases

Abstract Interval temporal logics take time intervals, instead of time instants, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval relations). In this paper, we compare and classify the expressiveness of all fragments of HS on the class of all linear orders and on the subclass of all dense linear orders. For each of these classes, we identify a complete set of definabilities between HS modalities, valid in that class, thus obtaining a complete classification of the family of all 4096 fragments of HS with respect to their expressiveness. We show that on the class of all linear orders there are exactly 1347 expressively different fragments of HS, while on the class of dense linear orders there are exactly 966 such expressively different fragments

An Optimal Decision Procedure for MPNL over the Integers

Interval temporal logics provide a natural framework for qualitative and quantitative temporal reason- ing over interval structures, where the truth of formulae is defined over intervals rather than points. In this paper, we study the complexity of the satisfiability problem for Metric Propositional Neigh- borhood Logic (MPNL). MPNL features two modalities to access intervals "to the left" and "to the right" of the current one, respectively, plus an infinite set of length constraints. MPNL, interpreted over the naturals, has been recently shown to be decidable by a doubly exponential procedure. We improve such a result by proving that MPNL is actually EXPSPACE-complete (even when length constraints are encoded in binary), when interpreted over finite structures, the naturals, and the in- tegers, by developing an EXPSPACE decision procedure for MPNL over the integers, which can be easily tailored to finite linear orders and the naturals (EXPSPACE-hardness was already known).Comment: In Proceedings GandALF 2011, arXiv:1106.081