Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function’s (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular as part of many learning algorithms, notably for neural networks. This paper uses Prolog to systematically derive gradient-based forward- and reverse-mode AD variants from a simple executable specification: evaluation of the symbolic derivative. Along the way we demonstrate that several Prolog features (DCGs, co-routines) contribute to the succinct formulation of the algorithm. We also discuss two applications in probabilistic programming that are enabled by our Prolog algorithms. The first is parameter learning for the Sum-Product Loop Language and the second consists of both parameter learning and variational inference for probabilistic logic programming.

Both hybrid automata and action languages are formalisms for describing the evolution of dynamic systems. This paper establishes a formal relationship between them. We show how to succinctly represent hybrid automata in an action language which in turn is defined as a high-level notation for answer set programming modulo theories—an extension of answer set programs to the first-order level similar to the way satisfiability modulo theories (SMT) extends propositional satisfiability (SAT). We first show how to represent linear hybrid automata with convex invariants by an action language modulo theories. A further translation into SMT allows for computing them using SMT solvers that support arithmetic over reals. Next, we extend the representation to the general class of non-linear hybrid automata allowing even non-convex invariants. We represent them by an action language modulo ordinary differential equations, which can be compiled into satisfiability modulo ordinary differential equations. We present a prototype system cplus2aspmt based on these translations, which allows for a succinct representation of hybrid transition systems that can be computed effectively by the state-of-the-art SMT solver dReal.

We propose a novel formal framework (called 3D-NCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-NCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and NCDC-ASP to 3D. 3D-NCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-NCDC-ASP, and illustrate its usefulness with applications.

The Logic Programming (LP) community, through the Association for Logic Programming (ALP) and its Executive Committee, decided to introduce for 2010 important changes in the way the main yearly results in LP and related areas are published. Whereas such results have appeared to date in standalone volumes of proceedings of the yearly International Conferences on Logic Programming (ICLP), and this method—fully in the tradition of Computer Science (CS)—has served the community well, it was felt that an effort needed to be made to achieve a higher level of compatibility with the publishing mechanisms of other fields outside CS.

Representing defeasibility is an important issue in common sense reasoning. In reasoning about action and change, this issue becomes more difficult because domain and action related defeasible information may conflict with general inertia rules. Furthermore, different types of defeasible information may also interfere with each other during the reasoning. In this paper, we develop a prioritized logic programming approach to handle defeasibilities in reasoning about action. In particular, we propose three action languages ${\cal AT}^{0}$, ${\cal AT}^{1}$, and ${\cal AT}^{2}$ which handle three types of defeasibilities in action domains named defeasible constraints, defeasible observations and actions with defeasible and abnormal effects respectively. Each language with a higher superscript can be viewed as an extension of the language with a lower superscript. These action languages inherit the simple syntax of ${\cal A}$ language but their semantics is developed in terms of transition systems where transition functions are defined based on prioritized logic programs. By illustrating various examples, we show that our approach eventually provides a powerful mechanism to handle various defeasibilities in temporal prediction and postdiction. We also investigate semantic properties of these three action languages and characterize classes of action domains that present more desirable solutions in reasoning about action within the underlying action languages.

A framework with sets of attacking arguments ($\textit{SETAF}$) is an extension of the well-known Dung’s Abstract Argumentation Frameworks ($\mathit{AAF}$s) that allows joint attacks on arguments. In this paper, we provide a translation from Normal Logic Programs ($\textit{NLP}$s) to $\textit{SETAF}$s and vice versa, from $\textit{SETAF}$s to $\textit{NLP}$s. We show that there is pairwise equivalence between their semantics, including the equivalence between $L$-stable and semi-stable semantics. Furthermore, for a class of $\textit{NLP}$s called Redundancy-Free Atomic Logic Programs ($\textit{RFALP}$s), there is also a structural equivalence as these back-and-forth translations are each other’s inverse. Then, we show that $\textit{RFALP}$s are as expressive as $\textit{NLP}$s by transforming any $\textit{NLP}$ into an equivalent $\textit{RFALP}$ through a series of program transformations already known in the literature. We also show that these program transformations are confluent, meaning that every $\textit{NLP}$ will be transformed into a unique $\textit{RFALP}$. The results presented in this paper enhance our understanding that $\textit{NLP}$s and $\textit{SETAF}$s are essentially the same formalism.

Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query in a suitable data structure, and using this data structure to compute the answer probability. Systems such as ProbLog, PITA, etc., use propositional data structures like explanation graphs, BDDs, SDDs, etc., to represent the possible worlds. While this approach saves inference time due to substructure sharing, there are a number of problems where a more compact data structure is possible. We propose a data structure called Ordered Symbolic Derivation Diagram (OSDD) which captures the possible worlds by means of constraint formulas. We describe a program transformation technique to construct OSDDs via query evaluation, and give procedures to perform exact and approximate inference over OSDDs. Our approach has two key properties. Firstly, the exact inference procedure is a generalization of traditional inference, and results in speedup over the latter in certain settings. Secondly, the approximate technique is a generalization of likelihood weighting in Bayesian Networks, and allows us to perform sampling-based inference with lower rejection rate and variance. We evaluate the effectiveness of the proposed techniques through experiments on several problems.

A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames has already been established. By “traditional” classes of frames, we mean those characterized by any positive combination of reflexivity, seriality, symmetry, transitivity, and the Euclidean property. In this paper, we fill the gaps remaining in an analogous classification of the graded modal language with graded converse modalities. In particular, we show its NExpTime-completeness over the class of Euclidean frames, demonstrating this way that over this class the considered language is harder than the language without graded modalities or without converse modalities. We also consider its variation disallowing graded converse modalities, but still admitting basic converse modalities. Our most important result for this variation is confirming an earlier conjecture that it is decidable over transitive frames. This contrasts with the undecidability of the language with graded converse modalities.

This paper describes how the Logic Programming System XSB combines top-down and bottom-up computation through the mechanisms of variant tabling and subsumptive tabling with abstraction, respectively.

It is well known that top-down evaluation of logical rules in Prolog has a procedural interpretation as recursive procedure invocation (Kowalski 1986). Tabling adds the intuition of short-circuiting redundant computations (Warren 1992). This paper shows how to introduce into tabled logic program evaluation a bottom-up component, whose procedural intuition is the initialization of a data structure, in which a relation is initially computed and filled, on first demand, and then used throughout the remainder of a larger computation for efficient lookup. This allows many Prolog programs to be expressed fully declaratively, programs which formerly required procedural features, such as assert, to be made efficient.

Malformed data-structures can lead to runtime errors such as arbitrary memory access or corruption. Despite this, reasoning over data-structure properties for low-level heap manipulating programs remains challenging. In this paper we present a constraint-based program analysis that checks data-structure integrity, w.r.t. given target data-structure properties, as the heap is manipulated by the program. Our approach is to automatically generate a solver for properties using the type definitions from the target program. The generated solver is implemented using a Constraint Handling Rules (CHR) extension of built-in heap, integer and equality solvers. A key property of our program analysis is that the target data-structure properties are shape neutral, i.e., the analysis does not check for properties relating to a given data-structure graph shape, such as doubly-linked-lists versus trees. Nevertheless, the analysis can detect errors in a wide range of data-structure manipulating programs, including those that use lists, trees, DAGs, graphs, etc. We present an implementation that uses the Satisfiability Modulo Constraint Handling Rules (SMCHR) system. Experimental results show that our approach works well for real-world C programs.

Automatic static cost analysis infers information about the resources used by programs without actually running them with concrete data and presents such information as functions of input data sizes. Most of the analysis tools for logic programs (and many for other languages), as CiaoPP, are based on setting up recurrence relations representing (bounds on) the computational cost of predicates and solving them to find closed-form functions. Such recurrence solving is a bottleneck in current tools: many of the recurrences that arise during the analysis cannot be solved with state-of-the-art solvers, including computer algebra systems (CASs), so that specific methods for different classes of recurrences need to be developed. We address such a challenge by developing a novel, general approach for solving arbitrary, constrained recurrence relations, that uses machine learning (sparse-linear and symbolic) regression techniques to guess a candidate closed-form function, and a combination of an SMT-solver and a CAS to check whether such function is actually a solution of the recurrence. Our prototype implementation and its experimental evaluation within the context of the CiaoPP system show quite promising results. Overall, for the considered benchmark set, our approach outperforms state-of-the-art cost analyzers and recurrence solvers and can find closed-form solutions, in a reasonable time, for recurrences that cannot be solved by them.

Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly studied logic programming fragment of ABA. In this work, we harness recent advances in incremental ASP solving for developing effective algorithms for reasoning tasks in the logic programming fragment of ABA that are presumably hard for the second level of the polynomial hierarchy, including skeptical reasoning under preferred semantics as well as preferential reasoning. In particular, we develop non-trivial counterexample-guided abstraction refinement procedures based on incremental ASP solving for these tasks. We also show empirically that the procedures are significantly more effective than previously proposed algorithms for the tasks.

An open ended list is a well known data structure in Prolog programs. It is frequently used to represent a value changing over time, while this value is referred to from several places in the data structure of the application. A weak point in this technique is that the time complexity is linear in the number of updates to the value represented by the open ended list. In this programming pearl we present a variant of the open ended list, namely an open ended tree, with an update and access time complexity logarithmic in the number of updates to the value.

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.

Technological progress in Answer Set Programming (ASP) has been stimulated by the use of common standards, such as the ASP-Core-2 language. While ASP has its roots in nonmonotonic reasoning, efforts have also been made to reconcile ASP with classical first-order (FO) logic. This has resulted in the development of FO(·), an expressive extension of FO, which allows ASP-like problem solving in a purely classical setting. This language may be more accessible to domain experts already familiar with FO and may be easier to combine with other formalisms that are based on classical logic. It is supported by the IDP inference system, which has successfully competed in a number of ASP competitions. Here, however, technological progress has been hampered by the limited number of systems that are available for FO(·). In this paper, we aim to address this gap by means of a translation tool that transforms an FO(·) specification into ASP-Core-2, thereby allowing ASP-Core-2 solvers to be used as solvers for FO(·) as well. We present experimental results to show that the resulting combination of our translation with an off-the-shelf ASP solver is competitive with the IDP system as a way of solving problems formulated in FO(·).

The World Wide Web is nowadays the most famous and widespread information system. Its success is witnessed by its enormous size and rate of growth: however, the same success of the Web has brought to a situation where more sophisticated techniques are urgently needed to properly handle this mass of information. In this sense, the more ambitious plan for an evolution of a Web is the so called Semantic Web, envisioned by the inventor of the Web itself, Tim Berners-Lee. In this architectural vision, there is the need for further layers of semantics, properly enriching the data that now overflow the classic Web: ontologies, rules, logic, proofs, trust are all ingredients of this ambitious picture. Given these premises, it should not come as a surprise the fact that this evolution is bringing the Web closer and closer to another field, that since quite some time has been facing similar problems of logical organization of knowledge: logic programming. Early examples, like the Metalog system in the World Wide Web Consortium (W3C), had shown that connecting logic programming and the Semantic Web was quite a natural and fruitful step: and in fact, the burst of research in Semantic Web developments has eventually started to touch, connect and reinterprete many topics that were and are mainstream of the logic programming area. We feel this is a necessary progression, as the Semantic Web, and more generally the Web of the future, has a lot to learn from research in the logic programming area. And, conversely, in these new scenarios there are lot of new applied problems that can be challenging and rewarding from a logic programming perspective. This calls for a tighter interaction between the Web and logic programming, which was the reason to motivate this special issue as well: gathering together a selection of the best contributions that could showcase the potential of the cross-breeding.

This paper looks at logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so that a soundness of the procedure is guaranteed in terms of 3-valued logic model theory.

This paper describes the development of the PALS system, an implementation of Prolog capable of efficiently exploiting or-parallelism on distributed-memory platforms—specifically Beowulf clusters. PALS makes use of a novel technique, called incremental stack-splitting. The technique proposed builds on the stack-splitting approach, previously described by the authors and experimentally validated on shared-memory systems, which in turn is an evolution of the stack-copying method used in a variety of parallel logic and constraint systems—e.g., MUSE, YAP, and Penny. The PALS system is the first distributed or-parallel implementation of Prolog based on the stack-splitting method ever realized. The results presented confirm the superiority of this method as a simple yet effective technique to transition from shared-memory to distributed-memory systems. PALS extends stack-splitting by combining it with incremental copying; the paper provides a description of the implementation of PALS, including details of how distributed scheduling is handled. We also investigate methodologies to effectively support order-sensitive predicates (e.g., side-effects) in the context of the stack-splitting scheme. Experimental results obtained from running PALS on both Shared Memory and Beowulf systems are presented and analyzed.

One of the differences among the various approaches to suspension-based tabled evaluation is the scheduling strategy. The two most popular strategies are local and batched evaluation. The former collects all the solutions to a tabled predicate before making any one of them available outside the tabled computation. The latter returns answers one by one before computing them all, which in principle is better if only one answer (or a subset of the answers) is desired. Batched evaluation is closer to SLD evaluation in that it computes solutions lazily as they are demanded, but it may need arbitrarily more memory than local evaluation, which is able to reclaim memory sooner. Some programs which in practice can be executed under the local strategy quickly run out of memory under batched evaluation. This has led to the general adoption of local evaluation at the expense of the more depth-first batched strategy. In this paper we study the reasons for the high memory consumption of batched evaluation and propose a new scheduling strategy which we have termed swapping evaluation. Swapping evaluation also returns answers one by one before completing a tabled call, but its memory usage can be orders of magnitude less than batched evaluation. An experimental implementation in the XSB system shows that swapping evaluation is a feasible memory-scalable strategy that need not compromise execution speed.