Abstract The Travelling Salesperson Problem (TSP) is a very well-known problem in computer science. Many real-world instances belong to the class of Euclidean TSP, in which the nodes to be visited lie on the Euclidean plane, and additional information is available with respect to the generic TSP, i.e. the coordinates of the nodes to be visited are known. In previous publications, we showed that the additional available information can be exploited to speed up the search, both in Constraint Logic Programming (CLP) and in Answer Set Programming (ASP). Constraint ASP (CASP) is a framework that joins CLP and ASP, and it aims at combining the features of both languages. In this article, we address the (Euclidean) TSP in CASP, and more specifically in the clingo$[DL]$ language and solver. We propose new encodings for the TSP in clingo$[DL]$; the new encodings are applicable to the general TSP (also to instances that are not Euclidean) and show a speedup of several orders of magnitude with respect to previous encodings. A further speedup can be obtained in Euclidean instances by exploiting geometric reasoning.

The growing demand for deployment of Artificial Intelligence (AI) on resource-constrained edge devices has motivated extensive research on the design of efficient edge-compatible AI hardware accelerators. One of the most promising solutions are the self-adaptive AI accelerators, capable of optimizing in real time their performance and energy consumption according to application requirements. This work introduces the EU-funded project Twinning for Excellence in Adaptive Edge Artificial Intelligence (AIDA4Edge), aimed to advance the state-of-the-art in the design of adaptive neural network accelerators for edge applications. The main goal is to develop a novel hybrid self-adaptive neural network architecture combining spiking and artificial neural networks, and supporting runtime adaptation of network functionality, precision and reliability. Furthermore, we aim to enhance the neural network training by incorporating hardware and quantization constraints in an automated tuning engine.

Abstract In the design of integrated circuits, one critical metric is the maximum delay introduced by combinational modules within the circuit. This delay is crucial because it represents the time required to perform a computation: in an Arithmetic Logic Unit, it represents the maximum time taken by the circuit to perform an arithmetic operation. When such a circuit is part of a larger, synchronous system, like a CPU, the maximum delay directly impacts the maximum clock frequency of the entire system. Typically, hardware designers use static timing analysis to compute an upper bound of the maximum delay because it can be determined in polynomial time. However, relying on this upper bound can lead to suboptimal processor speeds, thereby missing performance opportunities. In this work, we tackle the challenging task of computing the actual maximum delay, rather than an approximate value. Since the problem is computationally hard, we model it in answer set programming (ASP), a logic language featuring extremely efficient solvers. We propose non-trivial encodings of the problem into ASP. Experimental results show that ASP is a viable solution to address complex problems in hardware design.

Abstract Logic programming is a declarative programming paradigm that finds extensive use in the field of Artificial Intelligence (AI). As a result, it has become a valuable tool used in university courses for teaching students AI techniques. Besides Prolog language, the more recent Answer Set Programming (ASP) language turns out to be a powerful tool for developing advanced applications due to the expressiveness of the language and the availability of efficient solving systems. Unfortunately, the output of ASP solvers can be difficult to interpret, since it is a set of atoms, often long and verbose. This is most true in the case of students learning the language or in the case of experts developing applications for complex real-world problems. For these reasons, the ability to produce, when possible, a graphical representation of the solver output becomes useful to ensure easier interpretation of the results. In this paper we present ASPECT, a sub-language of ASP in which the user can directly define, in an intuitive and declarative way, a graphical representation of the answer set. The ASPECT atoms can be converted into the popular LaTeX markup language to produce vector graphics. The documents produced by ASPECT are easy to embed in documents such as scientific articles, course handouts and presentations. Also, the development of user-friendly interfaces is critical for wider use of similar technologies in the industrial sector as well. Moreover, ASPECT is also extended to deal with temporal information, and provide graphical animations of answer sets that enclose the temporal dimension, such as in planning problems. Finally, we advocate the use of ASPECT to create complex and animated presentations starting from a declarative specification.

Abstract Chronic patients suffering from non-communicable diseases are often enrolled into a diagnostic and therapeutic care program featuring a personalized care plan. Healthcare is mostly provided at the patient’s home, but those examinations and treatments that must be delivered at the hospital have to be explicitly booked. Booking is not trivial due to, on the one hand, the several time constraints that become particularly tight in the case of comorbidity, on the other hand, the limited availability of both staff and equipment at the hospital care units. This suggests that the scheduling of the clinical pathways for enrolled outpatients should be managed in a centralized manner, taking advantage of the fact that demand for services is known well in advance. The aim is to serve as many requests as possible (unattended requests are supplied by contracted private health facilities) in a timely manner, taking patients priority into account. Booking involves setting a date and a time for each selected health service, which is rather complex. In this work, we provide a declarative approach by encoding the problem in Answer Set Programming (ASP). In order to improve the scalability of the ASP approach, we present and compare two heuristic approaches, respectively based on service demand and time decomposition. All approaches are tested on instances of increasing size to assess scalability with respect to time horizon and number of requests.

Abstract In answer set programming (ASP), the user can define declaratively a problem and solve it with efficient solvers; practical applications of ASP are countless and several constraint problems have been successfully solved with ASP. On the other hand, solution time usually grows in a superlinear way (often, exponential) with respect to the size of the instance, which is impractical for large instances. A widely used approach is to split the optimization problem into subproblems (SPs) that are solved in sequence, some committing to the values assigned by others, and reconstructing a valid assignment for the whole problem by juxtaposing the solutions of the single SPs. On the one hand, this approach is much faster due to the superlinear behavior; on the other hand, it does not provide any guarantee of optimality: committing to the assignment of one SP can rule out the optimal solution from the search space. In other research areas, logic-Based Benders decomposition (LBBD) proved effective; in LBBD, the problem is decomposed into a master problem (MP) and one or several SPs. The solution of the MP is passed to the SPs that can possibly fail. In case of failure, a no-good is returned to the MP that is solved again with the addition of the new constraint. The solution process is iterated until a valid solution is obtained for all the SPs or the MP is proven infeasible. The obtained solution is provably optimal under very mild conditions. In this paper, we apply for the first time LBBD to ASP, exploiting an application in health care as case study. Experimental results show the effectiveness of the approach. We believe that the availability of LBBD can further increase the practical applicability of ASP technologies.

Abstract Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical models are a suitable framework to handle uncertain information, and in the last decade many probabilistic logical languages have been proposed, as well as inference and learning systems for them. In the realm of Abductive Logic Programming (ALP), a variety of proof procedures have been defined as well. In this paper, we consider a richer logic language, coping with probabilistic abduction with variables. In particular, we consider an ALP program enriched with integrity constraints à la IFF, possibly annotated with a probability value. We first present the overall abductive language and its semantics according to the Distribution Semantics. We then introduce a proof procedure, obtained by extending one previously presented, and prove its soundness and completeness.

The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science. The Euclidean TSP is a special case in which each node is identified by its coordinates on the plane and the Euclidean distance is used as cost function. Many works in the Constraint Programming (CP) literature addressed the TSP, and use as benchmark Euclidean instances; however the usual approach is to build a distance matrix from the points coordinates, and then address the problem as a TSP, disregarding the information carried by the points coordinates for constraint propagation. In this work, we propose to use geometric information, present in Euclidean TSP instances, to improve the filtering power. In order to have a declarative approach, we implemented the filtering algorithms in Constraint Logic Programming on Finite Domains (CLP(FD)).

Branching Algebra is the natural branching-time generalization of Allen’s Interval Algebra. As in the linear case, the consistency problem for Branching Algebra is NP-hard. Being relatively new, however, not much is known about the computational behaviour of the consistency problem of its sub-algebras, except in the case of the recently found subset of convex branching relations, for which the consistency of a network can be tested via path consistency and it is therefore deterministic polynomial. In this paper, following Nebel and Bürckert, we define the Horn fragment of Branching Algebra, and prove that it is a sub-algebra of the latter, being closed under inverse, intersection, and composition, that it strictly contains both the convex fragment of Branching Algebra and the Horn fragment of Interval Algebra, and that its consistency problem can be decided via path consistency. Finally, we experimentally prove that the Horn fragment of Branching Algebra can be used as an heuristic for checking the consistency of a generic network with a considerable improvement over the convex subset.

Abductive Logic Programming (ALP) has been proven very effective for formalizing societies of agents, commitments and norms, in particular by mapping the most common deontic operators (obligation, prohibition, permission) to abductive expectations. In our previous works, we have shown that ALP is a suitable framework for representing norms. Normative reasoning and query answering were accommodated by the same abductive proof procedure, named 𝒮CIFF. In this work, we introduce a defeasible flavour in this framework, in order to possibly discharge obligations in some scenarios. Abductive expectations can also be qualified as dischargeable, in the new, extended syntax. Both declarative and operational semantics are improved accordingly, and proof of soundness is given under syntax allowedness conditions Moreover, the dischargement itself might be proved invalid, or incoherent with the rules, due to new knowledge provided later on. In such a case, a discharged expectation might be reinstated and hold again after some evidence is given. We extend the notion of dischargement to take into consideration also the reinstatement of expectations. The expressiveness and power of the extended framework, named 𝒮CIFF𝒟, is shown by modeling and reasoning upon a fragment of the Japanese Civil Code. In particular, we consider a case study concerning manifestations of intention and their rescission (Section II of the Japanese Civil Code).

Silicon photonics is gaining momentum as a candidate technology platform for future intra- and inter-chip communications. However, its industrial uptake depends not only on technology maturity, but also on the capability to bridge the abstraction gap between technology developers and system designers. This paper presents an early-stage cross-layer refinement methodology of wavelength-routed optical network-on-chip topologies, linking logic topology synthesis to the physical implementation steps.

Allen's Interval Algebra (IA) is one of the most prominent formalisms in the area of qualitative temporal reasoning; however, its applications are naturally restricted to linear flows of time. When dealing with nonlinear time, Allen's algebra can be extended in several ways, and, as suggested by Ragni and Wölfl [M. Ragni and S. Wölfl, 2004], a possible solution consists in defining the Branching Algebra (BA) as a set of 19 basic relations (13 basic linear relations plus 6 new basic nonlinear ones) in such a way that each basic relation between two intervals is completely defined by the relative position of the endpoints on a tree-like partial order. While the problem of deciding the consistency of a network of IA-constraints is well-studied, and every subset of the IA has been classified with respect to the tractability of its consistency problem, the fragments of the BA have received less attention. In this paper, we first define the notion of convex BA-relation, and, then, we prove that the consistency of a network of convex BA-relations can be decided via path consistency, and is therefore a polynomial problem. This is the first non-trivial tractable fragment of the BA; given the clear parallel with the linear case, our contribution poses the bases for a deeper study of fragments of BA towards their complete classification.

The compliance verification task amounts to establishing if the execution of a system, given in terms of observed happened events, does respect a given property. In the past both the frameworks of Temporal Logics and Logic Programming have been extensively exploited to assess compliance in differen t domains, such as normative multi-agent systems, business process management and service oriented computing. In this work we review the LTL and SCIFF frameworks in the light of compliance evaluation, and formally investigate the relationship between the two approaches. We define a notion of compliance within each approach, and then we show that an arbitrary LTL formula can be expressed in SCIFF, by providing a translation procedure from LTL to SCIFF which preserves compliance.

Ontologies form the basis of the Semantic Web. Description Logics (DLs) are often the languages of choice for modeling ontologies. Integration of DLs with rules and rule-based reasoning is crucial in the so-called Semantic Web stack vision - a complete stack of recommendations and languages each ba sed on and/or exploiting the underlying layers - which adds new features to the standards used in theWeb. The growing importance of the integration between DLs and rules is proved by the definition of the profile OWL 2 RL1 and the definition of languages such as RIF2 and SWRL3. Datalog± is an extension of Datalog which can be used for representing lightweight ontologies and expressing some languages of the DL-Lite family, with tractable query answering under certain language restrictions. In particular, it is able to express the DL-Lite version defined in OWL. In this work, we show that Abductive Logic Programming (ALP) can be used to represent Datalog± ontologies, supporting query answering through an abductive proof procedure, and smoothly achieving the integration of ontologies and rule-based reasoning. Often, reasoning with DLs means finding explanations for the truth of queries, that are useful when debugging ontologies and to understand answers given by the reasoning process. We show that reasoning under existential rules can be expressed by ALP languages and we present a solving system, which is experimentally proved to be competitive with DL reasoning systems. In particular, we consider an ALP framework named 𝒮CIFF derived from the IFF abductive framework. Forward and backward reasoning is naturally supported in this ALP framework. The 𝒮CIFF language smoothly supports the integration of rules, expressed in a Logic Programming language, with Datalog± ontologies, mapped into 𝒮CIFF (forward) integrity constraints. The main advantage is that this integration is achieved within a single language, grounded on abduction in computational logic, and able to model existential rules.

Finding the entity responsible for an unpleasant situation is often difficult, especially in artificial agent societies. S CIFF is a formalization of agent societies, including a language to describe rules and protocols, and an abductive proof procedure for compliance checking. However, how to identify the entity responsible for a violation is not always clear. In this work, a definition of accountability for artificial societies is formalized in S CIFF. Two tools are provided for the designer of interaction protocols: a guideline, in terms of syntactic features that ensure accountability of the protocol, and an algorithm (implemented in a software tool) to investigate if, for a given protocol, nonaccountability issues could arise.

Abstract One promising trend in digital system integration consists of boosting on-chip communication performance by means of silicon photonics, thus materializing the so-called Optical Networks-on-Chip. Among them, wavelength routing can be used to route a signal to destination by univocally associating a routing path to the wavelength of the optical carrier. Such wavelengths should be chosen so to minimize interferences among optical channels and to avoid routing faults. As a result, physical parameter selection of such networks requires the solution of complex constrained optimization problems. In previous work, published in the proceedings of the International Conference on Computer-Aided Design, we proposed and solved the problem of computing the maximum parallelism obtainable in the communication between any two endpoints while avoiding misrouting of optical signals. The underlying technology, only quickly mentioned in that paper, is Answer Set Programming. In this work, we detail the Answer Set Programming approach we used to solve such problem. Another important design issue is to select the wavelengths of optical carriers such that they are spread across the available spectrum, in order to reduce the likelihood that, due to imperfections in the manufacturing process, unintended routing faults arise. We show how to address such problem in Constraint Logic Programming on Finite Domains.

The recent interest in emerging interconnect technologies is bringing the issue of a proper EDA support for them to the forefront, so to tackle the design complexity. A relevant case study is provided by wavelength-routed optical NoCs (WRONoCs), which add communication performance guarantees to the typical latency, throughput and power benefits of an optical link, thus providing an appealing technology for the photonic integration of high-end embedded systems. Typically, only abstract WRONoC models are considered to figure out architecture-level performance, and logic connectivity patterns for the quantification of the required signal strength (i.e., static power). However, this design practice overlooks the needed refinement step, where key physical parameters are assigned such as wavelengths of the optical channels, and size of the optical filters. This step is unfortunately not decoupled from the architectural evaluation, since its main constraint (i.e., avoiding routing faults) turns out to be a key limiter for both the network scale and the achievable communication parallelism. By proposing a formal methodology to select WRONoC parameters while avoding the routing fault concern, this paper aims at maximizing the levels of connectivity and/or of bit parallelism that WRONoCs can achieve, while relating their upper bounds to the uncertainty of the manufacturing process.

Positioning of valves is a real-life issue in Water Distribution System (WDS) design and, currently, it is usually addressed by hydraulic engineers either by hand or by means of genetic algorithms, that give no assurance of optimality. Since a given valves placement identifies a sectorization of the WDS in several isolable portions, the valves positioning problem can be seen as a variant of the well known graph partitioning problem, which is a hard combinatorial problem. Cattafi et al . (2011, TPLP , 11, 731–747) showed recently that Computational Logic can provide technologies and techniques that can be exploited to model and achieve the optimal partition of the water network (i.e. the optimal positioning of valves). In particular, the authors tackled the optimization of the valves positioning through a two player game model, giving a Constraint Logic Programming formalization to solve it effectively. The aim of this article, instead, is to investigate the potential of Answer Set Programming in this practical application; evaluation is in terms both of language expressivity and solving efficiency. Results are discussed for different ASP models and a comparison with the CLP(FD) technique shown by Cattafi et al . (2011, TPLP , 11, 731–747) will be given.

Designing sustainable energy policies has a strong impact on economy, society and environment. Beside a planning activity, policy makers are called to design a number of implementation instruments to enforce their plans. They encompass subsidies, fiscal incentives, feed in tariffs to name a few. Understanding the impact of these instruments on the energy market is essential to select the most efficient one. We propose in this paper a multi-agent simulator that mimics the adoption of photovoltaic as a consequence of a number of implementation instruments. The simulator mainly considers economic evaluations in the agent decision-making procedure, but we are aware also social aspects play an important role and they are subject of current research.

Abduction is a form of inference that supports hypothetical reasoning and has been applied to a number of domains, such as diagnosis, planning, protocol verification. Abductive Logic Programming (ALP) is the integration of abduction in logic programming. Usually, the operational semantics of an ALP language is defined as a proof procedure. The first implementations of ALP proof-procedures were based on the meta-interpretation technique, which is flexible but limits the use of the built-in predicates of logic programming systems. Another, more recent, approach exploits theoretical results on the similarity between abducibles and constraints. With this approach, which bears the advantage of an easy integration with built-in predicates and constraints, Constraint Handling Rules has been the language of choice for the implementation of abductive proof procedures. The first CHR-based implementation mapped integrity constraints directly to CHR rules, which is an efficient solution, but prevents defined predicates from being in the body of integrity constraints and does not allow a sound treatment of negation by default. In this paper, we describe the CHR-based implementation of the SCIFF abductive proof-procedure, which follows a different approach. The SCIFF implementation maps integrity constraints to CHR constraints, and the transitions of the proof-procedure to CHR rules, making it possible to treat default negation, while retaining the other advantages of CHR-based implementations of ALP proof-procedures.

This paper proposes to improve traditional what-if analysis for policy making by a novel integration of different components. When a simulator is available, a human expert, e.g., a policy maker, might understand the impact of her choices by running a simulator on a set of scenarios of interest. In many cases, when the number of scenarios is exponential in the number of choices, identifying the scenarios of interest might be particularly challenging. We claim that abandoning this generate and test approach could greatly enhance the decision process and the quality of political actions undertaken. In this paper we propose and experiment with one approach for combining simulation with a combinatorial optimization and decision making component. In addition, we propose two alternative approaches that can reasonably combine decision making with simulation in a coherent way and avoid the generate and test behaviour.

Theory and experimentation are two roots common to many scientific disciplines such as Physics, Medicine, and Computer Science. In all these disciplines theory and experimentation are tightly intertwined: they grow together and together make Science progress and evolve.

Biomass power plants are very promising for reducing carbon oxides emissions, because they provide energy with a carbon-neutral process. Biomass comes from trees and vegetables, so they provide a renewable type of energy. However, biomass plants location, along with their provisioning basins, are heavily regulated by economical aspects, often without careful consideration of their environmental footprint. For example, some Italian biomass plants import from overseas palm-tree oil that is economically convenient. However, the energy consumed for the oil transportation is definitely greater than the energy produced by the palm-tree oil burning. In this way biomass power plants turn out to be environmentally inefficient, even if they produce renewable energy. We propose an Integer Linear Programming approach for defining the energy and cost-efficient biomass plant location along with the corresponding provisioning basin. In addition, the model enables to evaluate existing plants and their energy and cost efficiency. Our study is based on real data gathered in the Emilia-Romagna region of Italy. Finally, this optimization tool is just a small part of a wider perspective that is aimed to define decision support tools for the improvement of regional planning and its precise strategic environmental assessment.

Abstract This paper presents a new application of logic programming to a real-life problem in hydraulic engineering. The work is developed as a collaboration of computer scientists and hydraulic engineers, and applies Constraint Logic Programming to solve a hard combinatorial problem. This application deals with one aspect of the design of a water distribution network, i.e., the valve isolation system design. We take the formulation of the problem by Giustolisi and Savić (2008 Optimal design of isolation valve system for water distribution networks. InProceedings of the 10th Annual Water Distribution Systems Analysis Conference WDSA2008, J. Van Zyl, A. Ilemobade, and H. Jacobs, Eds.) and show how, thanks to constraint propagation, we can get better solutions than the best solution known in the literature for the Apulian distribution network. We believe that the area of the so-calledhydroinformaticscan benefit from the techniques developed in Constraint Logic Programming and possibly from other areas of logic programming, such as Answer Set Programming.

After the enthusiasm of the fifties and early sixties, during which famous scientists predicted that computers would soon equal the human mind, Artificial Intelligence (A.I.) researchers had to face a bitter reality: many of the problems in A.I. have a combinatorial structure which requires the exploration of an exponential search space. The theory of NP-completeness added further discouragement to the great expectations of the previous decades. On the other hand, in the following years there was a plethora of new methodologies to address combinatorial problems that were published. Despite the discouraging complexity proofs based on worst-case analyses, practical algorithms were often able to address and solve real problems in reasonable time.

This special issue of Fundamenta Informaticae contains the revised, extended versions of selected \npapers presented at the Italian Conference on Computational Logic (Convegno Italiano di Logica Com- \nputazionale, CILC’09) which was held at the Engineering Department of the University of Ferrara, Italy.

Abstract Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the so-called coaxial matrices that define dependencies between plan activities (infrastructures, plants, resource extractions, buildings, etc.) and positive and negative environmental impacts, and dependencies between these impacts and environmental receptors. Up to now, this procedure is manually implemented by environmental experts for checking the environmental effects of a given plan or program, but it is never applied during the plan/program construction. A decision support system, based on a clear logic semantics, would be an invaluable tool not only in assessing a single, already defined plan, but also during the planning process in order to produce an optimized, environmentally assessed plan and to study possible alternative scenarios. We propose two logic-based approaches to the problem, one based on Constraint Logic Programming and one on Probabilistic Logic Programming that could be, in the future, conveniently merged to exploit the advantages of both. We test the proposed approaches on a real energy plan and we discuss their limitations and advantages.

In semantic Web technologies, searching for a service means to identify components that can potentially satisfy the user needs in terms of outputs and effects (discovery), and that, when invoked by the customer, can fruitfully interact with her (contracting). In this paper, we present an application framework that encompasses both the discovery and the contracting steps, in a unified search process. In particular, we accommodate service discovery by ontology-based reasoning, and contracting by automated reasoning about policies published in a formal language. To this purpose, we consider a formal approach grounded on computational logic, and abductive logic programming in particular. We propose a framework, called SCIFF reasoning engine, able to establish, by ontological and abductive reasoning, if a semantic Web service and a requester can fruitfully inter-operate, taking as input the behavioral interfaces of both the participants, and producing as output a sort of a contract.

ALP and Constraint Logic Programming (CLP) have been merged\nin works by various authors. However, while almost all\nCLP languages provide algorithms for finding an optimal solution\nwith respect to some objective function (and not just any solution),\nthe issue has received little attention in ALP. We believe that adding\noptimisation meta-predicates to abductive proof-procedures would\nimprove research and practical applications of abductive reasoning.

SCIFF is a framework thought to specify and verify interaction in open agent societies. The SCIFF language is equipped with a semantics based on abductive logic programming; SCIFF's operational component is a new abductive logic programming proof procedure, also named SCIFF, for reasoning with expectations in dynamic environments. In this article we present the declarative and operational semantics of the SCIFF language, and the termination, soundness, and completeness results of the SCIFF proof procedure, and we demonstrate SCIFF's possible application in the multiagent domain.

Although stemming from very different research areas, Multi-Agent Systems (MAS) and Service Oriented Computing (SOC) share common topics, problems and settings. One of the common problems is the need to formally verify the conformance of individuals (Agents or Web Services) to common rules and specifications (resp. Protocols/Choreographies), in order to provide a coherent behaviour and to reach the goals of the user.In previous publications, we developed a framework, SCIFF, for the automatic verification of compliance of agents to protocols. The framework includes a language based on abductive logic programming and on constraint logic programming for formally defining the social rules; suitable proof-procedures to check on-the-fly and a-priori the compliance of agents to protocols have been defined.Building on our experience in the MAS area, in this paper we make a first step towards the formal verification of web services conformance to choreographies. We adapt the SCIFF\ framework for the new settings, and propose a heir of SCIFF, the framework AlLoWS (Abductive Logic Web-service Specification).. AlLoWS comes with a language for defining formally a choreography and a web service specification. As its ancestor, AlLoWS has a declarative and an operational semantics. We show examples of how AlLoWS deals correctly with interaction patterns previously identified. Moreover, thanks to its constraint-based semantics, AlLoWS deals seamlessly with other cases involving constraints and deadlines

Constraint Logic Programming languages on Finite Domains, CLP( FD ), provide a declarative framework for Artificial Intelligence problems. However, in many real life cases, domains are not known and must be acquired or computed. In systems that interact with the outer world, domain elements synthesize information on the environment, they are not all known at the beginning of the computation, and must be retrieved through an expensive acquisition process.In this article, we extend the CLP( FD ) language by combining it with a new sort (called Incrementally specified Sets, I-Set ). In the resulting language, CLP( FD + I-Set ), FD variables can be defined on partially or fully unknown domains ( I-Set ). Domains can be linked each other through relations, and constraints can be imposed on them. We describe a propagation algorithm (called Known Arc Consistency (KAC)) based on known domain elements, and theoretically compare it with arc-consistency.The language can be implemented on top of different CLP systems, thus letting the user exploit different possible semantics for domains (e.g., lists, sets or streams). We state the specifications that the employed system should provide, and we show that two different CLP systems (Conjunto and { log }) can be effectively used.We provide motivating examples and describe promising applications.

In classical CLP(FD) systems, domains of variables are completely known at the beginning of the constraint propagation process. However, in systems interacting with an external environment, acquiring the whole domains of variables before the beginning of constraint propagation may cause waste of computation time, or even obsolescence of the acquired data at the time of use. For such cases, the Interactive Constraint Satisfaction Problem (ICSP) model has been proposed (Cucchiara et al. 1999a) as an extension of the CSP model, to make it possible to start constraint propagation even when domains are not fully known, performing acquisition of domain elements only when necessary, and without the need for restarting the propagation after every acquisition. In this paper, we show how a solver for the two sorted CLP language, defined in previous work (Gavanelli et al. 2005) to express ICSPs, has been implemented in the Constraint Handling Rules (CHR) language, a declarative language particularly suitable for high level implementation of constraint solvers.