Theory and Practice of Logic Programming - Latest issue

This special issue of Theory and Practice of Logic Programming (TPLP) contains the regular papers accepted for presentation at the 34-th International Conference on Logic Programming (ICLP 2018), held in Oxford, United Kingdom, from July 14th to July 17th, 2018.

Aggregates are among the most frequently used linguistic extensions of answer set programming. The result of an aggregation may introduce new constants during the instantiation of the input program, a feature known as value invention. When the aggregation involves literals whose truth value is undefined at instantiation time, modern grounders introduce several instances of the aggregate, one for each possible interpretation of the undefined literals. This paper introduces new data structures and techniques to handle such cases, and more in general aggregations on the same aggregate set identified in the ground program in input. The proposed solution reduces the memory footprint of the solver without sacrificing efficiency. On the contrary, the performance of the solver may improve thanks to the addition of some simple entailed clauses which are not easily discovered otherwise, and since redundant computation is avoided during propagation. Empirical evidence of the potential impact of the proposed solution is given.

Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting—among other reasoning modes—the central task of query answering. In the propositional case, query answering amounts to computing cautious consequences of the input program among the atoms in a given set of candidates, where a cautious consequence is an atom belonging to all stable models. Currently, the most efficient algorithms either iteratively verify the existence of a stable model of the input program extended with the complement of one candidate, where the candidate is heuristically selected, or introduce a clause enforcing the falsity of at least one candidate, so that the solver is free to choose which candidate to falsify at any time during the computation of a stable model. This paper introduces new algorithms for the computation of cautious consequences, with the aim of driving the solver to search for stable models discarding more candidates. Specifically, one of such algorithms enforces minimality on the set of true candidates, where different notions of minimality can be used, and another takes advantage of unsatisfiable cores computation. The algorithms are implemented in wasp, and experiments on benchmarks from the latest ASP competitions show that the new algorithms perform better than the state of the art.

Extending ASP with constraints (CASP) enhances its expressiveness and performance. This extension is not straightforward as the grounding phase, present in most ASP systems, removes variables and the links among them, and also causes a combinatorial explosion in the size of the program. Several methods to overcome this issue have been devised: restricting the constraint domains (e.g., discrete instead of dense), or the type (or number) of models that can be returned. In this paper we propose to incorporate constraints into s(ASP), a goal-directed, top-down execution model which implements ASP while retaining logical variables both during execution and in the answer sets. The resulting model, s(CASP), can constrain variables that, as in CLP, are kept during the execution and in the answer sets. s(CASP) inherits and generalizes the execution model of s(ASP) and is parametric w.r.t. the constraint solver. We describe this novel execution model and show through several examples the enhanced expressiveness of s(CASP) w.r.t. ASP, CLP, and other CASP systems. We also report improved performance w.r.t. other very mature, highly optimized ASP systems in some benchmarks.

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their paths. In this work, we propose two versions of a trajectory calculus based on the allowed properties over trajectories, where trajectories are defined as a sequence of non-overlapping regions of a partitioned map. More specifically, if a given trajectory is allowed to start and finish at the same region, 6 base relations are defined (TC-6). If a given trajectory should have different start and finish regions but cycles are allowed within, 10 base relations are defined (TC-10). Both versions of the calculus are implemented as ASP programs; we propose several different encodings, including a generalised program capable of encoding any qualitative calculus in ASP. All proposed encodings are experimentally evaluated using a real-world dataset. Experiment results show that the best performing implementation can scale up to an input of 250 trajectories for TC-6 and 150 trajectories for TC-10 for the problem of discovering a consistent configuration, a significant improvement compared to previous ASP implementations for similar qualitative spatial and temporal calculi.

We employ the Coq proof assistant to develop a mechanically-certified framework for evaluating graph queries and incrementally maintaining materialized graph instances, also called views. The language we use for defining queries and views is Regular Datalog (RD) – a notable fragment of non-recursive Datalog that can express complex navigational queries, with transitive closure as native operator. We first design and encode the theory of RD and then mechanize a RD-specific evaluation algorithm capable of fine-grained, incremental graph view computation, which we prove sound with respect to the declarative RD semantics. By using the Coq extraction mechanism, we test an OCaml version of the verified engine on a set of preliminary benchmarks. Our development is particularly focused on leveraging existing verification and notational techniques to: a) define mechanized properties that can be easily understood by logicians and database researchers and b) attain formal verification with limited effort. Our work is the first step towards a unified, machine-verified, formal framework for dynamic graph query languages and their evaluation engines.

In this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the syntax of First Order Logic with equality and the semantics of Quantified Equilibrium Logic with evaluable functions ( ${\rm QEL}^=_{\cal F}$ ). Then, we proceed to incorporate a new kind of logical term, intensional set (a construct commonly used to denote the set of objects characterised by a given formula), and to extend ${\rm QEL}^=_{\cal F}$ semantics for this new type of expression. In our extended approach, intensional sets can be arbitrarily used as predicate or function arguments or even nested inside other intensional sets, just as regular first-order logical terms. As a result, aggregates can be naturally formed by the application of some evaluable function (count, sum, maximum, etc) to a set of objects expressed as an intensional set. This approach has several advantages. First, while other semantics for aggregates depend on some syntactic transformation (either via a reduct or a formula translation), the ${\rm QEL}^=_{\cal F}$ interpretation treats them as regular evaluable functions, providing a compositional semantics and avoiding any kind of syntactic restriction. Second, aggregates can be explicitly defined now within the logical language by the simple addition of formulas that fix their meaning in terms of multiple applications of some (commutative and associative) binary operation. For instance, we can use recursive rules to define sum in terms of integer addition. Last, but not least, we prove that the semantics we obtain for aggregates coincides with the one defined by Gelfond and Zhang for the ${\cal A}\mathit{log}$ language, when we restrict to that syntactic fragment.

In this paper, we introduce an alternative approach to Temporal Answer Set Programming that relies on a variation of Temporal Equilibrium Logic (TEL) for finite traces. This approach allows us to even out the expressiveness of TEL over infinite traces with the computational capacity of (incremental) Answer Set Programming (ASP). Also, we argue that finite traces are more natural when reasoning about action and change. As a result, our approach is readily implementable via multi-shot ASP systems and benefits from an extension of ASP's full-fledged input language with temporal operators. This includes future as well as past operators whose combination offers a rich temporal modeling language. For computation, we identify the class of temporal logic programs and prove that it constitutes a normal form for our approach. Finally, we outline two implementations, a generic one and an extension of the ASP system clingo.

Under consideration for publication in Theory and Practice of Logic Programming (TPLP)

We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of the type hierarchy. We prove that there exists a bijection between such Fitting-monotonic functions and pairs of two-valued-result functions where the first member of the pair is monotone-antimonotone and the second member is antimonotone-monotone. By deriving an extension of consistent approximation fixpoint theory (Denecker et al. 2004) and utilizing the above bijection, we define an iterative procedure that produces for any given higher-order logic program a distinguished extensional model. We demonstrate that this model is actually a minimal one. Moreover, we prove that our construction generalizes the familiar well-founded semantics for classical logic programs, making in this way our proposal an appealing formulation for capturing the well-founded semantics for higher-order logic programs.

Conventional processor architectures are restricted in exploiting instruction level parallelism (ILP) due to the relatively low number of programmer-visible registers. Therefore, more recent processor architectures expose their datapaths so that the compiler (1) can schedule parallel instructions to different processing units and (2) can make effective use of local storage of the processing units. Among these architectures, the Synchronous Control Asynchronous Dataflow (SCAD) architecture is a new exposed datapath architecture whose processing units are equipped with first-in first-out (FIFO) buffers at their input and output ports.

In contrast to register-based machines, the optimal code generation for SCAD is still a matter of research. In particular, SAT and SMT solvers were used to generate optimal resource constrained and optimal time constrained schedules for SCAD, respectively. As Answer Set Programming (ASP) offers better flexibility in handling such scheduling problems, we focus in this paper on using an answer set solver for both resource and time constrained optimal SCAD code generation. As a major benefit of using ASP, we are able to generate all optimal schedules for a given program which allows one to study their properties. Furthermore, the experimental results of this paper demonstrate that the answer set solver can compete with SAT solvers and outperforms SMT solvers. This paper is under consideration for acceptance in TPLP.

We address the problem of verifying the satisfiability of Constrained Horn Clauses (CHCs) based on theories of inductively defined data structures, such as lists and trees. We propose a transformation technique whose objective is the removal of these data structures from CHCs, hence reducing their satisfiability to a satisfiability problem for CHCs on integers and booleans. We propose a transformation algorithm and identify a class of clauses where it always succeeds. We also consider an extension of that algorithm, which combines clause transformation with reasoning on integer constraints. Via an experimental evaluation we show that our technique greatly improves the effectiveness of applying the Z3 solver to CHCs. We also show that our verification technique based on CHC transformation followed by CHC solving, is competitive with respect to CHC solvers extended with induction.

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.

First-order resolution has been used for type inference for many years, including in Hindley-Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show that proof-relevant first-order resolution can play an important role in automating type inference and term synthesis for dependently typed languages. We propose a calculus that translates type inference and term synthesis problems in a dependently typed language to a logic program and a goal in the proof-relevant first-order Horn clause logic. The computed answer substitution and proof term then provide a solution to the given type inference and term synthesis problem. We prove the decidability and soundness of our method.

We introduce the asprilo1 framework to facilitate experimental studies of approaches addressing complex dynamic applications. For this purpose, we have chosen the domain of robotic intra-logistics. This domain is not only highly relevant in the context of today's fourth industrial revolution but it moreover combines a multitude of challenging issues within a single uniform framework. This includes multi-agent planning, reasoning about action, change, resources, strategies, etc. In return, asprilo allows users to study alternative solutions as regards effectiveness and scalability. Although asprilo relies on Answer Set Programming and Python, it is readily usable by any system complying with its fact-oriented interface format. This makes it attractive for benchmarking and teaching well beyond logic programming. More precisely, asprilo consists of a versatile benchmark generator, solution checker and visualizer as well as a bunch of reference encodings featuring various ASP techniques. Importantly, the visualizer's animation capabilities are indispensable for complex scenarios like intra-logistics in order to inspect valid as well as invalid solution candidates. Also, it allows for graphically editing benchmark layouts that can be used as a basis for generating benchmark suites.

Automated storage and retrieval systems are principal components of modern production and warehouse facilities. In particular, automated guided vehicles nowadays substitute human-operated pallet trucks in transporting production materials between storage locations and assembly stations. While low-level control systems take care of navigating such driverless vehicles along programmed routes and avoid collisions even under unforeseen circumstances, in the common case of multiple vehicles sharing the same operation area, the problem remains how to set up routes such that a collection of transport tasks is accomplished most effectively. We address this prevalent problem in the context of car assembly at Mercedes-Benz Ludwigsfelde GmbH, a large-scale producer of commercial vehicles, where routes for automated guided vehicles used in the production process have traditionally been hand-coded by human engineers. Such ad-hoc methods may suffice as long as a running production process remains in place, while any change in the factory layout or production targets necessitates tedious manual reconfiguration, not to mention the missing portability between different production plants. Unlike this, we propose a declarative approach based on Answer Set Programming to optimize the routes taken by automated guided vehicles for accomplishing transport tasks. The advantages include a transparent and executable problem formalization, provable optimality of routes relative to objective criteria, as well as elaboration tolerance towards particular factory layouts and production targets. Moreover, we demonstrate that our approach is efficient enough to deal with the transport tasks evolving in realistic production processes at the car factory of Mercedes-Benz Ludwigsfelde GmbH.

We describe an application of Answer Set Programming to the understanding of narratives about stereotypical activities, demonstrated via question answering. Substantial work in this direction was done by Erik Mueller, who modeled stereotypical activities as scripts. His systems were able to understand a good number of narratives, but could not process texts describing exceptional scenarios. We propose addressing this problem by using a theory of intentions developed by Blount, Gelfond, and Balduccini. We present a methodology in which we substitute scripts by activities (i.e., hierarchical plans associated with goals) and employ the concept of an intentional agent to reason about both normal and exceptional scenarios. We exemplify the application of this methodology by answering questions about a number of restaurant stories. This paper is under consideration for acceptance in TPLP.

We present a method for automatic inference of conditions on the initial states of a program that guarantee that the safety assertions in the program are not violated. Constrained Horn clauses (CHCs) are used to model the program and assertions in a uniform way, and we use standard abstract interpretations to derive an over-approximation of the set of unsafe initial states. The precondition then is the constraint corresponding to the complement of that set, under-approximating the set of safe initial states. This idea of complementation is not new, but previous attempts to exploit it have suffered from the loss of precision. Here we develop an iterative specialisation algorithm to give more precise, and in some cases optimal safety conditions. The algorithm combines existing transformations, namely constraint specialisation, partial evaluation and a trace elimination transformation. The last two of these transformations perform polyvariant specialisation, leading to disjunctive constraints which improve precision. The algorithm is implemented and tested on a benchmark suite of programs from the literature in precondition inference and software verification competitions.

Meta-Interpretive Learning (MIL) learns logic programs from examples by instantiating meta-rules, which is implemented by the Metagol system based on Prolog. Viewing MIL-problems as combinatorial search problems, they can alternatively be solved by employing Answer Set Programming (ASP), which may result in performance gains as a result of efficient conflict propagation. However, a straightforward ASP-encoding of MIL results in a huge search space due to a lack of procedural bias and the need for grounding. To address these challenging issues, we encode MIL in the HEX-formalism, which is an extension of ASP that allows us to outsource the background knowledge, and we restrict the search space to compensate for a procedural bias in ASP. This way, the import of constants from the background knowledge can for a given type of meta-rules be limited to relevant ones. Moreover, by abstracting from term manipulations in the encoding and by exploiting the HEX interface mechanism, the import of such constants can be entirely avoided in order to mitigate the grounding bottleneck. An experimental evaluation shows promising results.

Logic Programs with Ordered Disjunction (LPOD) is an extension of standard answer set programs to handle preference using the construct of ordered disjunction, and CR-Prolog2 is an extension of standard answer set programs with consistency restoring rules and LPOD-like ordered disjunction. We present reductions of each of these languages into the standard ASP language, which gives us an alternative way to understand the extensions in terms of the standard ASP language.

We present a probabilistic extension of action language ${\cal BC}$+$ . Just like ${\cal BC}$+$ is defined as a high-level notation of answer set programs for describing transition systems, the proposed language, which we call p ${\cal BC}$+$ , is defined as a high-level notation of LPMLN programs—a probabilistic extension of answer set programs. We show how probabilistic reasoning about transition systems, such as prediction, postdiction, and planning problems, as well as probabilistic diagnosis for dynamic domains, can be modeled in p ${\cal BC}$+$ and computed using an implementation of LPMLN.