The inexpressive Description Logic (DL) ${\cal F}{{\cal L}_0}$ , which has conjunction and value restriction as its only concept constructors, had fallen into disrepute when it turned out that reasoning in ${\cal F}{{\cal L}_0}$ w.r.t. general TBoxes is ExpTime-complete, that is, as hard as in the considerably more expressive logic ${\cal A}{\cal L}{\cal C}$ . In this paper, we rehabilitate ${\cal F}{{\cal L}_0}$ by presenting a dedicated subsumption algorithm for ${\cal F}{{\cal L}_0}$ , which is much simpler than the tableau-based algorithms employed by highly optimized DL reasoners. Our experiments show that the performance of our novel algorithm, as prototypically implemented in our ${\cal F}{{\cal L}_0}$ wer reasoner, compares very well with that of the highly optimized reasoners. ${\cal F}{{\cal L}_0}$ wer can also deal with ontologies written in the extension ${\cal F}{{\cal L}_ \bot }$ of ${\cal F}{{\cal L}_0}$ with the top and the bottom concept by employing a polynomial-time reduction, shown in this paper, which eliminates top and bottom. We also investigate the complexity of reasoning in DLs related to the Horn-fragments of ${\cal F}{{\cal L}_0}$ and ${\cal F}{{\cal L}_ \bot }$ .

Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive, is not purely model-theoretic. As a result, certain properties of programs appear non-trivial to formalize in purely logical terms. For example, the current characterization of strong equivalence for LPODs, does not coincide with logical equivalence in some specific logic. This comes in sharp contrast with the well-known characterization of strong equivalence for classical logic programs, which coincides with logical equivalence in the logic of here-and-there. In this paper we obtain a purely logical characterization of strong equivalence for LPODs as logical equivalence in a four-valued logic. Moreover, we provide a new proof of the coNP-completeness of strong equivalence for LPODs, which has an interest in its own right since it relies on the special structure of such programs. Our results are based on the recent logical semantics of LPODs, a fact which we believe indicates that this new semantics may prove to be a useful tool in the further study of LPODs.

Domain-specific languages (DSLs) are routinely created to simplify difficult or specialized programming tasks. They expose useful abstractions and design patterns in the form of language constructs, provide static semantics to eagerly detect misuse of these constructs, and dynamic semantics to completely define how language constructs interact. However, implementing and composing DSLs is a non-trivial task, and there is a lack of tools and techniques.

We address this problem by presenting a complete module system over LP for DSL construction, reuse, and composition. LP is already useful for DSL design, because it supports executable language specifications using notations familiar to language designers. We extend LP with a module system that is simple (with a few concepts), succinct (for key DSL specification scenarios), and composable (on the level of languages, compilers, and programs). These design choices reflect our use of LP for industrial DSL design. Our module system has been implemented in the formula language, and was used to build key Windows 8 device drivers via DSLs. Though we present our module system as it actually appears in our formula language, our emphasis is on concepts adaptable to other LP languages.

We consider disjunctive logic programs without function symbols but with existential quantification in rule heads, under the semantics of general stable models. There are at least two interesting prospects in these programs. The first is that a program can be made more succinct by using existential variables, and the second is on the potential in representing defeasible ontological knowledge by these logic programs. This paper studies some of the properties of these programs. First, we show a simple yet intuitive definition of stable models for these programs that does not resort to second-order logic. Second, the stable models of these programs can be characterized by an extension of progression for disjunctive programs, which provides a native characterization of justification for stable models. We then study the decidability issue. While the stable model existence problem for safe disjunctive programs is decidable, with existential quantification allowed in rule heads the problem becomes undecidable. We identify an interesting decidable fragment by exploring a new notion of stratification over existential quantification.

Answer set programming is a prominent declarative programming paradigm used in formulating combinatorial search problems and implementing different knowledge representation formalisms. Frequently, several related and yet substantially different answer set programs exist for a given problem. Sometimes these encodings may display significantly different performance. Uncovering precise formal links between these programs is often important and yet far from trivial. This paper presents formal results carefully relating a number of interesting program rewritings. It also provides the proof of correctness of system projector concerned with automatic program rewritings for the sake of efficiency.

Epistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice, ELPs are often written in a modular way, where each module interacts with other modules by accepting sets of facts as input, and passing on sets of facts as output. An interesting question then presents itself: under which conditions can such a module be replaced by another one without changing the outcome, for any set of input facts? This problem is known as uniform equivalence, and has been studied extensively for ASP. For ELPs, however, such an investigation is, as of yet, missing. In this paper, we therefore propose a characterization of uniform equivalence that can be directly applied to the language of state-of-the-art ELP solvers. We also investigate the computational complexity of deciding uniform equivalence for two ELPs, and show that it is on the third level of the polynomial hierarchy.

We study here schedulers for a class of rules that naturally arise in the context of rule-based constraint programming. We systematically derive a scheduler for them from a generic iteration algorithm of Apt (2000). We apply this study to so-called membership rules of Apt and Monfroy (2001). This leads to an implementation that yields a considerably better performance for these rules than their execution as standard CHR rules. Finally, we show how redundant rules can be identified and how appropriately reduced sets of rules can be computed.

As an invited contributor to this Festschrift honoring Alain Colmerauer, I feel compelled to give not only an account of his main research contributions, but also of my perspective on the motivations behind them. I hope that this will provide the reader with a glimpse of how a focused, tenacious, rigorous, and inventive mind like Alain's picks research problems and proceeds to solve them. The history of Prolog, the language that remains one of Alain's major accomplishments, is well documented. His paper on the ‘Birth of Prolog,’ co-authored with Philippe Roussel (Colmerauer & Roussel, 1970), is a highly recommended account of the circumstances that led to the development of Prolog. Bob Kowalski (1988) presents his views of the early history of Prolog from the automatic theorem proving perspective. Finally, my own paper on the topic (Cohen, 1988) contains material complementing Alain's and Bob's narratives. Instead of recasting already-available historical material, I have opted to present here a more personal account of Alain's contributions, acknowledging in advance the individual bias inherent in such an accounting of long-past events.

Meseguer's rewriting logic and the rewriting logic CRWL are two well-known approaches to rewriting as logical deduction that, despite some clear similarities, were designed with different objectives. Here we study the relationships between them, both at a syntactic and at a semantic level. Even though it is not possible to establish an entailment system map between them, both can be naturally simulated in each other. Semantically, there is no embedding between the corresponding institutions. Along the way, the notions of entailment and satisfaction in Meseguer's rewriting logic are generalized.

The development of complex software requires tools promoting fail-fast approaches, so that bugs and unexpected behavior can be quickly identified and fixed. Tools for data validation may save the day of computer programmers. In fact, processing invalid data is a waste of resources at best, and a drama at worst if the problem remains unnoticed and wrong results are used for business. Answer Set Programming (ASP) is not an exception, but the quest for better and better performance resulted in systems that essentially do not validate data. Even under the simplistic assumption that input/output data are eventually validated by external tools, invalid data may appear in other portions of the program, and go undetected until some other module of the designed software suddenly breaks. This paper formalizes the problem of data validation for ASP programs, introduces a language to specify data validation, and presents valasp, a tool to inject data validation in ordinary programs. The proposed approach promotes fail-fast techniques at coding time without imposing any lag on the deployed system if data are pretended to be valid. Validation can be specified in terms of statements using YAML, ASP and Python. Additionally, the proposed approach opens the possibility to use ASP for validating data of imperative programming languages.

Logic Production System (LPS) is a logic-based framework for modelling reactive behaviour. Based on abductive logic programming, it combines reactive rules with logic programs, a database and a causal theory that specifies transitions between the states of the database. This paper proposes a systematic mapping of the Kernel of this framework (called KELPS) into an answer set program (ASP). For this purpose a new variant of KELPS with finite models, called n-distance KELPS, is introduced. A formal definition of the mapping from this n-distance KELPS to ASP is given and proven sound and complete. The Answer Set Programming paradigm allows to capture additional behaviours to the basic reactivity of KELPS, in particular proactive, pre-emptive and prospective behaviours. These are all discussed and illustrated with examples. Then a hybrid framework is proposed that integrates KELPS and ASP, allowing to combine the strengths of both paradigms.

Logic programming is a powerful paradigm for programming autonomous agents in dynamic domains as witnessed by languages such as Golog and Flux. In this work we present ALPprolog, an expressive, yet efficient, logic programming language for the online control of agents that have to reason about incomplete information and sensing actions.

This special issue marks the tenth anniversary of the LOPSTR workshop. LOPSTR started in 1991 as a workshop on Logic Program Synthesis and Transformation, but later it broadened its scope to logic-based Program Development in general.

The motivating force behind LOPSTR has been a belief that declarative paradigms such as logic programming are better suited to program development tasks than traditional non-declarative ones such as the imperative paradigm. Specification, synthesis, transformation or specialisation, analysis, verification and debugging can all be given logical foundations, thus providing a unifying framework for the whole development process.

In the past ten years or so, such a theoretical framework has indeed begun to emerge. Even tools have been implemented for analysis, verification and specialisation. However, it is fair to say that so far the focus has largely been on programming-in-the-small. So the future challenge is to apply or extend these techniques to programming-in-the-large, in order to tackle software engineering in the real world.

In this note, we use Kunen’s notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate p that are consequences of the program. The first theorem identifies a class of programs for which the well-founded and Fitting semantics coincide for the positive part of p. The second theorem shows that if a program has a signing, then computing the positive part of p under the well-founded semantics requires the computation of only one part of each predicate. This theorem suggests an analysis for query answering under the well-founded semantics. In the process of proving these results, we use an alternative formulation of the well-founded semantics of logic programs, which might be of independent interest.

Goal-level Independent and-parallelism (IAP) is exploited by scheduling for simultaneous execution of two or more goals, which will not interfere with each other at run time. This can be done safely even if such goals can produce multiple answers. The most successful IAP implementations to date have used recomputation of answers and sequentially ordered backtracking. While in principle simplifying the implementation, recomputation can be very inefficient if the granularity of the parallel goals is large enough and they produce several answers, while sequentially ordered backtracking limits parallelism. And, despite the expected simplification, the implementation of the classic schemes has proved to involve complex engineering, with the consequent difficulty for system maintenance and extension, while still frequently running into the well-known trapped goal and garbage slot problems. This work presents an alternative parallel backtracking model for IAP and its implementation. The model features parallel out-of-order (i.e., nonchronological) backtracking and relies on answer memoization to reuse and combine answers. We show that this approach can bring significant performance advantages. Also, it can bring some simplification to the important engineering task involved in implementing the backtracking mechanism of previous approaches.

Researchers working on the automatic parallelization of programs have long known that too much parallelism can be even worse for performance than too little, because spawning a task to be run on another CPU incurs overheads. Autoparallelizing compilers have therefore long tried to use granularity analysis to ensure that they only spawn off computations whose cost will probably exceed the spawn-off cost by a comfortable margin. However, this is not enough to yield good results, because data dependencies may also limit the usefulness of running computations in parallel. If one computation blocks almost immediately and can resume only after another has completed its work, then the cost of parallelization again exceeds the benefit. We present a set of algorithms for recognizing places in a program where it is worthwhile to execute two or more computations in parallel that pay attention to the second of these issues as well as the first. Our system uses profiling information to compute the times at which a procedure call consumes the values of its input arguments and the times at which it produces the values of its output arguments. Given two calls that may be executed in parallel, our system uses the times of production and consumption of the variables they share to determine how much their executions would overlap if they were run in parallel, and therefore whether executing them in parallel is a good idea or not. We have implemented this technique for Mercury in the form of a tool that uses profiling data to generate recommendations about what to parallelize, for the Mercury compiler to apply on the next compilation of the program. We present preliminary results that show that this technique can yield useful parallelization speedups, while requiring nothing more from the programmer than representative input data for the profiling run.

M. Bezem defined an extensional semantics for positive higher-order logic programs. Recently, it was demonstrated by Rondogiannis and Symeonidou that Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values. Rondogiannis and Symeonidou also demonstrated that Bezem's technique, when extended under the stable model semantics, does not in general lead to extensional stable models. In this paper, we consider the problem of extending Bezem's technique under the well-founded semantics. We demonstrate that the well-founded extension fails to retain extensionality in the general case. On the positive side, we demonstrate that for stratified higher-order logic programs, extensionality is indeed achieved. We analyze the reasons of the failure of extensionality in the general case, arguing that a three-valued setting cannot distinguish between certain predicates that appear to have a different behaviour inside a program context, but which happen to be identical as three-valued relations.

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this article, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful computations and rich forms of abstractions, including higher-order programming, modularity, and abstract data types. Term-level bindings are another kind of abstraction, and these are given an elegant and direct treatment within both proof theory and these extended logic programming languages. Logic programming has also inspired new results in proof theory, such as those involving polarity and focused proofs. These recent results provide a high-level means for presenting the differences between forward-chaining and backward-chaining style inferences. Anchoring logic programming in proof theory has also helped identify its connections and differences with functional programming, deductive databases, and model checking.

Describing complex objects by elementary ones is a common strategy in mathematics and science in general. In their seminal 1965 paper, Kenneth Krohn and John Rhodes showed that every finite deterministic automaton can be represented (or “emulated”) by a cascade product of very simple automata. This led to an elegant algebraic theory of automata based on finite semigroups (Krohn-Rhodes Theory). Surprisingly, by relating logic programs and automata, we can show in this paper that the Krohn-Rhodes Theory is applicable in Answer Set Programming (ASP). More precisely, we recast the concept of a cascade product to ASP, and prove that every program can be represented by a product of very simple programs, the reset and standard programs. Roughly, this implies that the reset and standard programs are the basic building blocks of ASP with respect to the cascade product. In a broader sense, this paper is a first step towards an algebraic theory of products and networks of nonmonotonic reasoning systems based on Krohn-Rhodes Theory, aiming at important open issues in ASP and AI in general.