Stable models of logic programs have been studied and characterized in relation with other formalisms by many researchers. As already argued in previous papers, such characterizations are interesting for diverse reasons, including theoretical investigations and the possibility of leading to new algorithms for computing stable models of logic programs. At the theoretical level, complexity and expressiveness comparisons have brought about fundamental insights. Beyond that, practical implementations of the developed reductions enable the use of existing solvers for other logical formalisms to compute stable models. In this paper, we first provide a simple characterization of stable models that can be viewed as a proof-theoretic counterpart of the standard model-theoretic definition. We further show how it can be naturally encoded in difference logic. Such an encoding, compared to the existing reductions to classical logics, does not require Boolean variables. Then, we implement our novel translation to a Satisfiability Modulo Theories (SMT) formula. We finally compare our approach, employing the SMT solver yices, to the translation-based ASP solver lp2diff and to clingo on domains from the “Basic Decision” track of the 2017 Answer Set Programming competition. The results show that our approach is competitive to and often better than lp2diff, and that it can also be faster than clingo on non-tight domains.

The Optimal In-Station Train Dispatching (InSTraDi) problem consists in commanding the movements of trains inside a railway station while both (i) respecting safety, time, and travel constraints and (ii) minimizing delays. In Symbolic Pattern Planning (SPP), a pattern, suggesting the sequence of happenings to reach the goal, is encoded in a logic formula whose models correspond to valid plans. If no valid plan is found, the pattern is extended until it covers a valid plan. However, plans of better quality could exist if we had continued extending the pattern. In this paper, we formalize the InSTraDi problem as a Temporal Planning Task with Intermediate Conditions and Effects, and we show an InSTraDi-dependent way to construct, in polynomial time, a pattern ensuring the optimal plan can be found by the SPP approach without never extending the pattern. Analysis on realistic railway data validate our approach.

In this paper, we propose a novel approach for solving automated planning problems, called Symbolic Pattern Planning. Given a deterministic planning problem Π, we propose to compute a plan by first fixing a pattern –defined as an arbitrary sequence of actions– and then define a formula encoding the state resulting from the sequential execution of the actions in the pattern, starting from an arbitrary initial state. By allowing each action in the pattern to be executed consecutively zero, one or possibly more times, and by imposing the conditions on the initial and goal states, we can check whether the pattern allows determining a valid plan or whether the pattern needs to be extended and the procedure iterated. We ground our proposal in the numeric planning setting, we prove the correctness and also the completeness of the procedure (provided at each iteration the pattern is extended with a complete sequence of actions), and we define procedures for the pattern selection and for computing quality plans. When exploiting the planning as satisfiability approach, we show that our encoding allows to determine a valid plan in a number of iterations which is never higher than the one needed by the state-of-the-art rolled-up or relaxed-relaxed-∃ symbolic encodings. On the experimental side, we run an extensive analysis which included the problems and systems involved in the numeric track of the 2023 International Planning Competition, showing that the results validate the theoretical findings and that our planner Patty has remarkably good comparative performances.

We consider temporal numeric planning problems Π expressed in PDDL2.1, and show how it is possible to produce SMT formulas (i) whose models correspond to valid plans of Π, and (ii) which extends the recently proposed planning with patterns approach from the numeric to the temporal case. We prove the correctness and completeness of the approach and that it outperforms all the publicly available temporal planners on 10 domains with required concurrency.

In classical planning, conditional effects (CEs) allow modelling non-idempotent actions, where the resulting state may depend on how many times each action is consecutively repeated. Though CEs have been widely studied in the literature, no one has ever studied how to exploit rolling, i.e., how to effectively model the consecutive repetition of an action. In this paper, we fill this void by (i) showing that planning with CEs remains PSPACE-complete even in the limit case of problems with a single action, (ii) presenting a correct and complete planning as satisfiability encoding exploiting rolling while effectively dealing with constraints imposed on the set of reachable states, and (iii) theoretically and empirically showing its substantial benefits.

In this paper, we present a symbolic search-based procedure for numeric planning based on Symbolic Pattern Planning (SPP). In SPP, a pattern is a sequence of actions used to define a logic formula whose models correspond to sequences of applicable actions and reachable states. Here, starting from the empty pattern, we iteratively extend and compress it using search techniques until a goal state is reached. We prove the correctness and completeness of the procedure and demonstrate its good performance compared to both the original SPP approach and other publicly available numeric planners on the 2023 International Planning Competition Agile track.

Stable models of logic programs have been studied and characterized in relation with other formalisms by many researchers. As already argued in previous papers, such characterizations are interesting for diverse reasons, including theoretical investigations and the possibility of leading to new algorithms for computing stable models of logic programs. At the theoretical level, complexity and expressiveness comparisons have brought about fundamental insights. Beyond that, practical implementations of the developed reductions enable the use of existing solvers for other logical formalisms to compute stable models. In this paper, we first provide a simple characterization of stable models that can be viewed as a proof-theoretic counterpart of the standard model-theoretic definition. We further show how it can be naturally encoded in difference logic. Such an encoding, compared to the existing reductions to classical logics, does not require Boolean variables. Then, we implement our novel translation to a Satisfiability Modulo Theories (SMT) formula. We finally compare our approach, employing the SMT solver yices , to the translation-based ASP solver lp2diff and to clingo on domains from the “Basic Decision” track of the 2017 Answer Set Programming competition. The results show that our approach is competitive to and often better than lp2diff , and that it can also be faster than clingo on non-tight domains.

In this paper, we propose a novel approach for solving linear numeric planning problems, called Symbolic Pattern Planning. Given a planning problem Pi, a bound n and a pattern --defined as an arbitrary sequence of actions-- we encode the problem of finding a plan for Pi with bound n as a formula with fewer variables and/or clauses than the state-of-the-art rolled-up and relaxed-relaxed-exists encodings. More importantly, we prove that for any given bound, it is never the case that the latter two encodings allow finding a valid plan while ours does not. On the experimental side, we consider 6 other planning systems --including the ones which participated in this year's International Planning Competition (IPC)-- and we show that our planner Patty has remarkably good comparative performances on this year's IPC problems.

The objective of this work is to develop computational cognitive models embedded in a humanoid robot. We focus on Dark Triad constructs and the so-called “Nice and Nasty” Theory of Mind that have never been investigated through a robotic approach. To this end, DT and ToM conceptual models in psychology have been taken as a reference for developing a framework based on the popular PDDL planning language. Next, a cognitive architecture has been implemented on a humanoid robot, with the final objective of making adverse personalities emerge. The motivations of the present work are both theoretical and practical. On the one side, we aim to provide researchers with new insights into DT constructs through simulated and robotic setups. On the other side, we aim to provide a tool to train psychologists to deal with social and antisocial behaviour in a controlled setup. The article includes all the details about the model and the experiments performed.

We consider the problem of planning with arithmetic theories, and focus on generating optimal plans for numeric domains with constant and state-dependent action costs. Solving these problems efficiently requires a seamless integration between propositional and numeric reasoning. We propose a novel approach that leverages Optimization Modulo Theories (OMT) solvers to implement a domain-independent optimal theory-planner. We present a new encoding for optimal planning in this setting and we evaluate our approach using well-known, as well as new, numeric benchmarks.

Twelve years have elapsed since the first Quantified Boolean Formulas (QBFs) evaluation was held as an event linked to SAT conferences. During this period, researchers have striven to propose new algorithms and tools to solve challenging formulas, with evaluations periodically trying to assess the current state of the art. In this paper, we present an experimental account of solvers and formulas with the aim to understand the progress in the QBF arena across these years. Unlike typical evaluations, the analysis is not confined to the snapshot of submitted solvers and formulas, but rather we consider several tools that were proposed over the last decade, and we run them on different formulas from previous QBF evaluations. The main contributions of our analysis, which are also the messages we would like to pass along to the research community, are: (i) many formulas that turned out to be difficult to solve in past evaluations, remain still challenging after twelve years, (ii) there is no single solver which can significantly outperform all the others, unless specific categories of formulas are considered, and (iii) effectiveness of preprocessing depends both on the coupled solver and the structure of the formula.

In this paper we present the parallel QBF Solver PaQuBE. This new solver leverages the additional computational power that can be exploited from modern computer architectures, from pervasive multi-core boxes to clusters and grids, to solve more relev

Planning as Satisfiability is one of the most well-known and effective techniques for classical planning: satplan has been the winning system in the deterministic track for optimal planners in the 4th International Planning Competition (IPC) and a cowinner in the 5th IPC. Given a planning problem П and a makespan n, the approach based on satisfiability (a.k.a. SAT-based) simply works by (i) constructing a SAT formula П n and (ii) checking Ðn for satisfiability: if there is a model for П n then we have found a plan, otherwise n is increased. The approach guarantees that the makespan is optimal, i.e. minimum. In this article we extend the Planning as Satisfiability approach in order to handle preferences and satplan in order to solve problems with simple preferences. This allows, e.g. to take into consideration ‘plan quality’ issues other than makespan, like number of actions and ‘soft’ goals. The basic idea is to explore the search space of possible plans in accordance with the given partially ordered preferences.We first prove that, at fixed makespan, our approach returns an ‘optimal’ plan, if any. Then, considering both classical planning problems and problems coming from IPC-5, we show that satplan extended in order to deal with preferences: (i) returns optimal plans that are often of considerable better quality, i.e. with fewer actions or with a better plan metric on soft goals, than satplan; and (ii) is overall competitive, in terms of plan quality, with sgplan, the winning system in the ‘SimplePreferences’ category of the IPC-5. Notably, such results are often obtained without sacrificing efficiency.

ERTMS is the European Railway Traffic Management System. The CENELEC EN50128 guidelines for software development of safety critical system require that the software produced is verified by providing a set of tests covering the 100% of the code. This requirement, however, substantially increases the costs associated to the testing phase, since it may involve the manual generation of tests. In this paper we present a methodology to automatic generate test achieving the desired code coverage. The automatization of the test generation phase, applied to some modules of the ERTMS developed by Ansaldo STS (an Italian leading company in the field), led to a dramatic increase in the productivity and to a reduction of the costs of the entire software development process.

The problem of expressing and solving satisfiability problems (SAT) with qualitative preferences is central in many areas of Computer Science and Artificial Intelligence. In previous papers, it has been shown that qualitative preferences on literals allow for capturing qualitative/quantitative preferences on literals/formulas; and that an optimal model for a satisfiability problems with qualitative preferences on literals can be computed via a simple modification of the Davis-Logemann-Loveland procedure (DLL): Given a SAT formula, an optimal solution is computed by simply imposing that DLL branches according to the partial order on the preferences. Unfortunately, it is well known that introducing an ordering on the branching heuristic of DLL may cause an exponential degradation in its performances. The experimental analysis reported in these papers hightlights that such degradation can indeed show up in the presence of a significant number of preferences.

The best currently available solvers for quantified Boolean formulas (QBFs) process their input in prenex form, i.e., all the quantifiers have to appear in the prefix of the formula separated from the purely propositional part representing the matrix. However, in many QBFs derived from applications, the propositional part is intertwined with the quantifier structure. To tackle this problem, the standard approach is to convert such QBFs in prenex form, thereby losing structural information about the prefix. In the case of search-based solvers, the prenex-form conversion introduces additional constraints on the branching heuristic and reduces the benefits of the learning mechanisms. In this paper, we show that conversion to prenex form is not necessary: current search-based solvers can be naturally extended in order to handle nonprenex QBFs and to exploit the original quantifier structure. We highlight the two mentioned drawbacks of the conversion in prenex form with a simple example, and we show that our ideas can also be useful for solving QBFs in prenex form. To validate our claims, we implemented our ideas in the state-of-the-art search-based solver QuBE and conducted an extensive experimental analysis. The results show that very substantial speedups can be obtained

The best currently available solvers for quantified Boolean formulas (QBFs) process their input in prenex form, i.e., all the quantifiers have to appear in the prefix of the formula separated from the purely proppositional part representing the matrix. However, in many QBFs deriving from applications, the propositional part is intertwined with the quantifier structure. To tackle this problem, the standard approach is to first convert them in prenex form, thereby loosing structural information about the prefix. In this paper we show that conversion to prenex form is not necessary, i.e., that it is relatively easy to extend current search based solvers in order to exploit the original quantifier structure, i.e., to handle non prenex QBFs. Further, we show that the conversion can lead to the exploration of search spaces bigger than the space explored by solvers handling non prenex QBFs. To validate our claims, we implemented our ideas in the state-of-the-art search based solver QuBE, and conducted an extensive experimental analysis. The results show that very substantial speedups can be obtained

Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as a set of clauses. Deduction starts by inferring new clauses by resolution, and goes on until the empty clause is generated or satisfiability of the set of clauses is proven, e.g., because no new clauses can be generated. In this paper, we restrict our attention to the problem of evaluating Quantified Boolean Formulas (QBFs). In this setting, the above outlined deduction process is known to be sound and complete if given a formula in CNF and if a form of resolution, called ``Q-resolution'', is used. We introduce Q-resolution on terms, to be used for formulas in disjunctive normal form. We show that the computation performed by most of the available procedures for QBFs --based on the Davis-Logemann-Loveland procedure (DLL) for propositional satisfiability-- corresponds to a tree in which Q-resolution on terms and clauses alternate. This poses the theoretical bases for the introduction of learning, corresponding to recording Q-resolution formulas associated with the nodes of the tree. We discuss the problems related to the introduction of learning in DLL based procedures, and present solutions extending state-of-the-art proposals coming from the literature on propositional satisfiability. Finally, we show that our DLL based solver extended with learning, performs significantly better on benchmarks used in the 2003 QBF solvers comparative evaluation.

Abstract. Answer Set Programming (ASP) and propositional satisfiability (SAT) are closely related. In some recent work we have shown that, on a wide set of logic programs called “tight”, the main search procedures used by ASP and SAT systems are equivalent, i.e., that they explore search trees with the same branching nodes. In this paper, we focus on the experimental evaluation of different search strategies, heuristics and their combinations that have been shown to be effective in the SAT community, in ASP systems. Our results show that, despite the strong link between ASP and SAT, it is not always the case that search strategies, heuristics and/or their combinations that currently dominate in SAT are also bound to dominate in ASP. We provide a detailed experimental evaluation for this phenomenon and we shed light on future development of efficient Answer Set solvers. 1

The goal of this paper is to provide a formalization of monotonic belief and belief about belief in a multiagent environment. We distinguish between ideal beliefs, i.e. those beliefs which satisfy certain ‘idealized’ properties which are unlikely to be possessed by real agents, and real beliefs. Our formalization is based on a set‐theoretic specification of beliefs and, then, on the definition of the appropriate constructors which intentionally present the sets identified. This allows us to provide a uniform and taxonomic characterization of the possible ways in which ideal and real beliefs can arise. We compare our notion of ideal with the notion of logical omniscience from the modal literature, and show that the first is much weaker and more granular than the second. We provide intuitions about the conceptual importance of the cases analysed by proving and discussing some equivalence results with some important modal systems modelling (non) logical omniscience.

The goal of this paper is to present a logical framework for the formalization of agents' mutual beliefs in a Multi Agent system. The approach is based on a combination of extensional specifications of beliefs and context-based (finite) presentation of the specifications by employing a particular class of Multi Context systems. The extensional specification provides a set-theoretic characterization of beliefs in terms of sets closed under certain conditions. Its finite presentation is provided by using as constructors inference rules inside a Multi Context system. The resulting framework allows for capturing many relevant cases of real (not omniscient) agents, which are very common in Multi Agent scenarios embedded in real world environments. In order to substantiate this claim, two Multi Agent scenarios are formally specified in detail in the specification framework. ©1999 John Wiley & Sons, Inc.

Generality and locality have been proposed as two crucial properties for systems formalizing common-sense reasoning. The first is the ability of representing knowledge in a way that makes it usable in a wide class of circumstances. The second is the ability of using only a subset of the potentially available knowledge, namely the subset which is held to be relevant in a given circumstance. These two properties seem to be one the opposite of the other, since disregarding part of the available information (locality) may lead to a loss of generality. In this paper, we argue that this is not the case, and propose a general methodology for combining generality and locality. This methodology is essentially based on the notion of context. As a case study, we propose a formalization of the Glasgow-London-Moscow example and its mechanization in an interactive theorem prover, GETFOL.

We are mainly interested in the development of CAD systems for interior design. An effective use of such systems relies to a large extent on the characteristics of their user interface. This paper describes NALIG, a system able to "understand" and "reason about" high level descriptions of spatial scenes. The user interacts with the system by using a natural language interface which, though very simple, is expressive enough to allow the description of complex configurations of objects. NALIG replies by drawing on the screen an image mirroring its own "understanding" of the scene described. The comprehension process has required the integration of different AI-techniques (e.g., natural language understanding, spatial reasoning, default and common sense reasoning).

We propose multicontext systems (MC systems) as a formal framework for the specification of complex reasoning. MC systems provide the ability to structure the specification of “global” reasoning in terms of “local” reasoning subpatterns. Each subpattern is modeled as a deduction in a context, formally defined as an axiomatic formal system. the global reasoning pattern is modeled as a concatenation of contextual deductions via bridge rules, i.e., inference rules that infer a fact in one context from facts asserted in other contexts. Besides the formal framework, in this article we propose a three-layer architecture designed to specify and automatize complex reasoning. At the first level we have object-level contexts (called s-contexts) for domain specifications. Problem-solving principles and, more in general, meta-level knowledge about the application domain is specified in a distinct context, called Problem-Solving Context (PSC). On top of s-contexts and PSC, we have a further context, called MT, where it is possible to specify strategies to control multicontext reasoning spanning through s-contexts and PSC. We show how GETFOL can be used as a computer tool for the implementation of MC systems and for the automatization of multicontext deductions. © 1995 John Wiley & Sons, Inc.