The transformation logics

We introduce a new family of temporal logics designed to finely balance the trade-off between expressivity and complexity. Their key feature is the possibility of defining operators of a new kind that we call transformation operators. Some of them subsume existing temporal operators, while others are entirely novel. Of particular interest are transformation operators based on semigroups. They enable logics to harness the richness of semigroup theory, and we show them to yield logics capable of creating hierarchies of increasing expressivity and complexity which are non-trivial to characterise in existing logics. The result is a genuinely novel and yet unexplored landscape of temporal logics, each of them with the potential of matching the trade-off between expressivity and complexity required by specific applications

The Krohn-Rhodes Logics

We present a new family of modal temporal logics of the past, obtained by extending Past LTL with a rich set of temporal operators based on the theory by Krohn and Rhodes for automata cascades. The theory says that every automaton can be expressed as a cascade of some basic automata called prime automata. They are the building blocks of all automata, analogously to prime numbers being the building blocks of all natural numbers. We show that Past LTL corresponds to cascades of one kind of prime automata called flip-flops. In particular, the temporal operators of Past LTL are captured by flip-flops, and they cannot capture any other prime automaton, confining the expressivity within the star-free regular languages. We propose novel temporal operators that can capture other prime automata, and hence extend the expressivity of Past LTL. Such operators are infinitely-many, and they yield an infinite number of logics capturing an infinite number of distinct fragments of the regular languages. The result is a yet unexplored landscape of extensions of Past LTL, that we call Krohn-Rhodes Logics, each of them with the potential of matching the expressivity required by specific applications

On the expressivity of recurrent neural cascades with identity

Recurrent Neural Cascades (RNC) are the class of recurrent neural networks with no cyclic dependencies among recurrent neurons. Their subclass RNC+ with positive recurrent weights has been shown to be closely connected to the starfree regular languages, which are the expressivity of many well-established temporal logics. The existing expressivity results show that the regular languages captured by RNC+ are the star-free ones, and they leave open the possibility that RNC+ may capture languages beyond regular. We exclude this possibility for languages that include an identity element, i.e., an input that can occur an arbitrary number of times without affecting the output. Namely, in the presence of an identity element, we show that the languages captured by RNC+ are exactly the star-free regular languages. Identity elements are ubiquitous in temporal patterns, and hence our results apply to a large number of applications. The implications of our results go beyond expressivity. At their core, we establish a close structural correspondence between RNC+ and semiautomata cascades, showing that every neuron can be equivalently captured by a three-state semiautomaton. A notable consequence of this result is that RNC+ are no more succinct than cascades of three-state semiautomata

Stream Reasoning in Temporal Datalog

In recent years, there has been an increasing interest in extending traditional stream processing engines with logical, rule-based, reasoning capabilities. This poses significant theoretical and practical challenges since rules can derive new information and propagate it both towards past and future time points; as a result, streamed query answers can depend on data that has not yet been received, as well as on data that arrived far in the past. Stream reasoning algorithms, however, must be able to stream out query answers as soon as possible, and can only keep a limited number of previous input facts in memory. In this paper, we propose novel reasoning problems to deal with these challenges, and study their computational properties on Datalog extended with a temporal sort and the successor function (a core rule-based language for stream reasoning applications)

Improved Answer-Set Programming Encodings for Abstract Argumentation

The design of efficient solutions for abstract argumentation problems is a crucial step towards advanced argumentation systems. One of the most prominent approaches in the literature is to use Answer-Set Programming (ASP) for this endeavor. In this paper, we present new encodings for three prominent argumentation semantics using the concept of conditional literals in disjunctions as provided by the ASP-system clingo. Our new encodings are not only more succinct than previous versions, but also outperform them on standard benchmarks.Comment: To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 201

Automata cascades: expressivity and sample complexity

Every automaton can be decomposed into a cascade of basic prime automata. This is the Prime Decomposition Theorem by Krohn and Rhodes. Guided by this theory, we propose automata cascades as a structured, modular, way to describe automata as complex systems made of many components, each implementing a specific functionality. Any automaton can serve as a component; using specific components allows for a fine-grained control of the expressivity of the resulting class of automata; using prime automata as components implies specific expressivity guarantees. Moreover, specifying automata as cascades allows for describing the sample complexity of automata in terms of their components. We show that the sample complexity is linear in the number of components and the maximum complexity of a single component, modulo logarithmic factors. This opens to the possibility of learning automata representing large dynamical systems consisting of many parts interacting with each other. It is in sharp contrast with the established understanding of the sample complexity of automata, described in terms of the overall number of states and input letters, which implies that it is only possible to learn automata where the number of states is linear in the amount of data available. Instead our results show that one can learn automata with a number of states that is exponential in the amount of data available

The Window Validity Problem in Rule-Based Stream Reasoning

Rule-based temporal query languages provide the expressive power and flexibility required to capture in a natural way complex analysis tasks over streaming data. Stream processing applications, however, typically require near real-time response using limited resources. In particular, it becomes essential that the underpinning query language has favourable computational properties and that stream processing algorithms are able to keep only a small number of previously received facts in memory at any point in time without sacrificing correctness. In this paper, we propose a recursive fragment of temporal Datalog with tractable data complexity and study the properties of a generic stream reasoning algorithm for this fragment. We focus on the window validity problem as a way to minimise the number of time points for which the stream reasoning algorithm needs to keep data in memory at any point in time

Provably efficient offline reinforcement learning in regular decision processes

This paper deals with offline (or batch) Reinforcement Learning (RL) in episodic Regular Decision Processes (RDPs). RDPs are the subclass of Non-Markov Decision Processes where the dependency on the history of past events can be captured by a finite-state automaton. We consider a setting where the automaton that underlies the RDP is unknown, and a learner strives to learn a near-optimal policy using pre-collected data, in the form of non-Markov sequences of observations, without further exploration. We present RegORL, an algorithm that suitably combines automata learning techniques and state-of-the-art algorithms for offline RL in MDPs. RegORL has a modular design allowing one to use any off-the-shelf offline RL algorithm in MDPs. We report a non-asymptotic high-probability sample complexity bound for RegORL to yield an ε-optimal policy, which makes appear a notion of concentrability relevant for RDPs. Furthermore, we present a sample complexity lower bound for offline RL in RDPs. To our best knowledge, this is the first work presenting a provably efficient algorithm for offline learning in RDPs

STRUCTURAL ANALYSIS FOR AN HISTORICAL R.C. TALL BUILDING RESTORATION

n this paper a detailed structural analysis (under the seismic and wind loads) of an historical tall building in Milan is carried out. It’s one of the first tall building (109 m height) realized in Italy in the 56- 59 years, and an important restoration is affecting it with intended use change (from office to luxury hotel and residences). To investigate the characteristics of concrete several destructive, non-destructive and combined tests are conducted. Moreover, additional destructive and chemical tests on the reinforced bars steel are performed too. Some finite elements models (FEMs) are implemented by using beam and plate elements considering two different boundary conditions (base fixed and elastic soil by Winkler model) and the interaction of the close existing lower constructions presence. In all of the FEMs, the materials characteristics are assigned basing on the tests results and a their subsequent statistical interpretation. The seismic load, implemented by a response spectrum analysis, and the wind load are applied in according to the Italian Construction Code (NTC). The structural resistance verifies are carried out in terms of shear and combined compressive-bending stress, whereas further ductility verifies are conducted considering appropriate nonlinear behaviours of the concrete and the steel bars. Finally some hypothesis to improve the structural behaviour under the lateral loads are proposed by considering cost-benefit analysis

Temporal Logic Monitoring Rewards via Transducers

In Markov Decision Processes (MDPs), rewards are assigned according to a function of the last state and action. This is often limiting, when the considered domain is not naturally Markovian, but becomes so after careful engineering of extended state space. The extended states record information from the past that is sufficient to assign rewards by looking just at the last state and action. Non-Markovian Reward Decision Processes (NRMDPs) extend MDPs by allowing for non-Markovian rewards, which depend on the history of states and actions. Non-Markovian rewards can be specified in temporal logics on finite traces such as LTLf/LDLf, with the great advantage of a higher abstraction and succinctness; they can then be automatically compiled into an MDP with an extended state space. We contribute to the techniques to handle temporal rewards and to the solutions to engineer them. We first present an approach to compiling temporal rewards which merges the formula automata into a single transducer, sometimes saving up to an exponential number of states. We then define monitoring rewards, which add a further level of abstraction to temporal rewards by adopting the four-valued conditions of runtime monitoring; we argue that our compilation technique allows for an efficient handling of monitoring rewards. Finally, we discuss application to reinforcement learning