Extension Of Answer Set Programming Research Articles

Aspmc: New frontiers of algebraic answer set counting

In the last decade, there has been increasing interest in extensions of answer set programming (ASP) that cater for quantitative information such as weights or probabilities. A wide range of quantitative reasoning tasks for ASP and logic programming, among them probabilistic inference and parameter learning in the neuro-symbolic setting, can be expressed as algebraic answer set counting (AASC) tasks, i.e., weighted model counting for ASP with weights calculated over some semiring, which makes efficient solvers for AASC desirable. In this article, we present ▪, a new solver for AASC that pushes the limits of efficient solvability. Notably, ▪ provides improved performance compared to the state of the art in probabilistic inference by exploiting three insights gained from thorough theoretical investigations in our work. Namely, we consider the knowledge compilation step in the AASC pipeline, where the underlying logical theory specified by the answer set program is converted into a tractable circuit representation, on which AASC is feasible in polynomial time. First, we provide a detailed comparison of different approaches to knowledge compilation for programs, revealing that translation to propositional formulas followed by compilation to sd-DNNF seems favorable. Second, we study how the translation to propositional formulas should proceed to result in efficient compilation. This leads to the second and third insight, namely a novel way of breaking the positive cyclic dependencies in a program, called TP-Unfolding, and an improvement to the Clark Completion, the procedure used to transform programs without positive cyclic dependencies into propositional formulas. Both improvements are tailored towards efficient knowledge compilation. Our empirical evaluation reveals that while all three advancements contribute to the success of ▪, TP-Unfolding improves performance significantly by allowing us to handle cyclic instances better.

Metric dynamic equilibrium logic

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behaviour of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. In many applications, however, timing constraints are important like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time Dynamic Equilibrium Logic, in which dynamic operators are constrained by intervals over integers. The resulting Metric Dynamic Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. As such, it constitutes the most general among a whole spectrum of temporal extensions of Equilibrium Logic. In detail, we show that it encompasses Temporal, Dynamic, Metric and regular Equilibrium Logic, as well as its classic counterparts once the law of the excluded middle is added.

Evaluating Epistemic Logic Programs via Answer Set Programming with Quantifiers

In this paper we introduce a simple way to evaluate epistemic logic programs by means of answer set programming with quantifiers, a recently proposed extension of answer set programming. The method can easily be adapted for most of the many semantics that were proposed for epistemic logic programs. We evaluate the proposed transformation on existing benchmarks using a recently proposed solver for answer set programming with quantifiers, which relies on QBF solvers.

Answer-Set Programming for Lexicographical Makespan Optimisation in Parallel Machine Scheduling

AbstractWe deal with a challenging scheduling problem on parallel machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated machines, thus few machines can determine the makespan almost regardless of how jobs are scheduled on the remaining ones. This causes problems when machines fail and jobs need to be rescheduled. Instead of optimising only the makespan, we put the individual machine spans in non-ascending order and lexicographically minimise the resulting tuples. This achieves that all machines complete as early as possible and increases the robustness of the schedule. We study the application of answer-set programming (ASP) to solve this problem. While ASP eases modelling, the combination of timing constraints and the considered objective function challenges current solving technology. The former issue is addressed by using an extension of ASP by difference logic. For the latter, we devise different algorithms that use multi-shot solving. To tackle industrial-sized instances, we study different approximations and heuristics. Our experimental results show that ASP is indeed a promising knowledge representation and reasoning (KRR) paradigm for this problem and is competitive with state-of-the-art constraint programming (CP) and Mixed-Integer Programming (MIP) solvers.

Automata Techniques for Temporal Answer Set Programming

Temporal and dynamic extensions of Answer Set Programming (ASP) have played an important role in addressing dynamic problems, as they allow the use of temporal operators to reason with dynamic scenarios in a very effective way. In my Ph.D. research, I intend to exploit the relationship between automata theory and dynamic logic to add automata-based techniques to the ASP solver CLINGO helping us to deal with theses type of problems.

Quantitative and Stream Extensions of Answer Set Programming

Answer Set Programming has separately been extended with constraints, to the streaming domain, and with capabilities to reason over the quantities associated with answer sets. We propose the introduction and analysis of a general framework that incorporates all three directions of extension by exploiting the strengths of Here-and-There Logic and Weighted Logic.

Planning with Incomplete Information in Quantified Answer Set Programming

AbstractWe present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.

Determining Action Reversibility in STRIPS Using Answer Set and Epistemic Logic Programming

AbstractIn the context of planning and reasoning about actions and change, we call an action reversible when its effects can be reverted by applying other actions, returning to the original state. Renewed interest in this area has led to several results in the context of the PDDL language, widely used for describing planning tasks. In this paper, we propose several solutions to the computational problem of deciding the reversibility of an action. In particular, we leverage an existing translation from PDDL to Answer Set Programming (ASP), and then use several different encodings to tackle the problem of action reversibility for the STRIPS fragment of PDDL. For these, we use ASP, as well as Epistemic Logic Programming (ELP), an extension of ASP with epistemic operators, and compare and contrast their strengths and weaknesses.

Reasoning on Multirelational Contextual Hierarchies via Answer Set Programming with Algebraic Measures

AbstractDealing with context-dependent knowledge has led to different formalizations of the notion of context. Among them is the Contextualized Knowledge Repository (CKR) framework, which is rooted in description logics but links on the reasoning side strongly to logic programs and Answer Set Programming (ASP) in particular. The CKR framework caters for reasoning with defeasible axioms and exceptions in contexts, which was extended to knowledge inheritance across contexts in a coverage (specificity) hierarchy. However, the approach supports only this single type of contextual relation and the reasoning procedures work only for restricted hierarchies, due to nontrivial issues with model preference under exceptions. In this paper, we overcome these limitations and present a generalization of CKR hierarchies to multiple contextual relations, along with their interpretation of defeasible axioms and preference. To support reasoning, we use ASP with algebraic measures, which is a recent extension of ASP with weighted formulas over semirings that allows one to associate quantities with interpretations depending on the truth values of propositional atoms. Notably, we show that for a relevant fragment of CKR hierarchies with multiple contextual relations, query answering can be realized with the popular asprin framework. The algebraic measures approach is more powerful and enables, for example, reasoning with epistemic queries over CKRs, which opens interesting perspectives for the use of quantitative ASP extensions in other applications.

A Unifying Approach for Nonmonotonic S4F, (Reflexive) Autoepistemic Logic, and Answer Set Programming

This paper presents a general strategy, bringing together some major types of nonmonotonic reasoning under a monotonic bimodal setting. Such formalisms are also of interest to the fields of knowledge representation and declarative programming. We exemplify the methodology, capturing minimal model reasoning that underlies nonmonotonicity over S4F first, but then we also show how to apply the technique to other nonmonotonic logics respectively based on the modal logics KD45 and SW5. We naturally succeed it, by modifying only the axioms of the underlying modal logic and show that it successfully works. The last two formalisms are also known as autoepistemic logic (AEL) and its reflexive extension (RAEL) in the given order: AEL is an important form of nonmonotonic reasoning, introduced by Robert C. Moore in order to allow an agent to reason about his own knowledge. Equilibrium logic (EL) is a general-purpose nonmonotonic reasoning formalism, proposed more recently by David Pearce as a semantical framework for answer set programming (ASP). The latter is an efficient declarative problem solving approach with lots of applications to science and technology. Fariñas et al. have embedded EL (and so ASP) into a monotonic bimodal logic. We take this work as an initiative and successfully apply a similar methodology to closely aligned nonmonotonic modal logics. We finally discuss the potential capability to subsume the epistemic extensions of ASP within our unified paradigm.

Extending Answer Set Programs with Neural Networks

The integration of low-level perception with high-level reasoning is one of the oldest problems in Artificial Intelligence. Recently, several proposals were made to implement the reasoning process in complex neural network architectures. While these works aim at extending neural networks with the capability of reasoning, a natural question that we consider is: can we extend answer set programs with neural networks to allow complex and high-level reasoning on neural network outputs? As a preliminary result, we propose NeurASP -- a simple extension of answer set programs by embracing neural networks where neural network outputs are treated as probability distributions over atomic facts in answer set programs. We show that NeurASP can not only improve the perception accuracy of a pre-trained neural network, but also help to train a neural network better by giving restrictions through logic rules. However, training with NeurASP would take much more time than pure neural network training due to the internal use of a symbolic reasoning engine. For future work, we plan to investigate the potential ways to solve the scalability issue of NeurASP. One potential way is to embed logic programs directly in neural networks. On this route, we plan to first design a SAT solver using neural networks, then extend such a solver to allow logic programs.

Splitting a Hybrid ASP Program

Hybrid Answer Set Programming (Hybrid ASP) is an extension of Answer Set Programming (ASP) that allows ASP-like rules to interact with outside sources. The Splitting Set Theorem is an important and extensively used result for ASP. The paper introduces the Splitting Set Theorem for Hybrid ASP, which is for Hybrid ASP the equivalent of the Splitting Set Theorem, and shows how it can be applied to simplify computing answer sets for Hybrid ASP programs most relevant for practical applications.

Autoepistemic answer set programming

Defined by Gelfond in 1991, epistemic specifications constitute an extension of Answer Set Programming (ASP) that introduces subjective literals. A subjective literal allows checking whether some regular literal is true in all (or in some of) the answer sets of the program, that are further collected in a set called world view. One epistemic program may yield several world views but, under the original semantics, some of them resulted from self-supported derivations. During the last eight years, several alternative approaches have been proposed to get rid of these self-supported world views. Unfortunately, their success could only be measured by studying their behaviour on a set of common examples in the literature, since no formal property of “self-supportedness” had been defined. To fill this gap, we extend in this paper the idea of unfounded set from standard logic programming to the epistemic case. We define when a world view is founded with respect to some program. Accordingly, we define the foundedness property for an arbitrary semantics, so it holds when its world views are always founded. Using counterexamples, we explain that the previous approaches violate foundedness, and proceed to propose a new semantics based on a combination of Moore's Autoepistemic Logic and Pearce's Equilibrium Logic. This combination paves the way for the development of an autoepistemic extension of ASP. The main result proves that this new semantics precisely captures the set of world views of the original semantics that are founded.

Towards Metric Temporal Answer Set Programming

AbstractWe elaborate upon the theoretical foundations of a metric temporal extension of Answer Set Programming. In analogy to previous extensions of ASP with constructs from Linear Temporal and Dynamic Logic, we accomplish this in the setting of the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic. More precisely, we develop our logic on the same semantic underpinnings as its predecessors and thus use a simple time domain of bounded time steps. This allows us to compare all variants in a uniform framework and ultimately combine them in a common implementation.

Selp: A Single-Shot Epistemic Logic Program Solver

AbstractEpistemic logic programs (ELPs) are an extension of answer set programming (ASP) with epistemic operators that allow for a form of meta-reasoning, that is, reasoning over multiple possible worlds. Existing ELP solving approaches generally rely on making multiple calls to an ASP solver in order to evaluate the ELP. However, in this paper, we show that there also exists a direct translation from ELPs into non-ground ASP with bounded arity. The resulting ASP program can thus be solved in a single shot. We then implement this encoding method, using recently proposed techniques to handle large, non-ground ASP rules, into the prototype ELP solving system “selp,” which we present in this paper. This solver exhibits competitive performance on a set of ELP benchmark instances.

Epistemic Logic Programs: A Different World View

Epistemic Logic Programs (ELPs), an extension of Answer Set Programming (ASP) with epistemic operators, have received renewed attention from the research community in recent years. Classically, evaluating an ELP yields a set of world views, with each being a set of answer sets. In this paper, we propose an alternative definition of world views that represents them as three-valued assignments, where each atom can be either always true, always false, or neither. Based on several examples, we show that this definition is natural and intuitive. We also investigate relevant computational properties of these new semantics, and explore how other notions, like strong equivalence, are affected.

Strong Equivalence for LPMLN Programs

LPMLN is a probabilistic extension of answer set programs with the weight scheme adapted from Markov Logic. We study the concept of strong equivalence in LPMLN, which is a useful mathematical tool for simplifying a part of an LPMLN program without looking at the rest of it. We show that the verification of strong equivalence in LPMLN can be reduced to equivalence checking in classical logic via a reduct and choice rules as well as to equivalence checking under the "soft" logic of here-and-there. The result allows us to leverage an answer set solver for LPMLN strong equivalence checking. The study also suggests us a few reformulations of the LPMLN semantics using choice rules, the logic of here-and-there, and classical logic.

A parallel memory-efficient epistemic logic program solver: harder, better, faster

As the practical use of answer set programming (ASP) has grown with the development of efficient solvers, we expect a growing interest in extensions of ASP as their semantics stabilize and solvers supporting them mature. Epistemic Specifications, which adds modal operators K and M to the language of ASP, is one such extension. We call a program in this language an epistemic logic program (ELP). Solvers have thus far been practical for only the simplest ELPs due to exponential growth of the search space. We describe a solver that, at the time of its development (mid-2016), was able to solve harder problems better (e.g., without exponentially-growing memory needs w.r.t. K and M occurrences) and faster than any other known ELP solver.

Inlining External Sources in Answer Set Programs

Abstracthex-programs are an extension of answer set programs (ASP) with external sources. To this end, external atoms provide a bidirectional interface between the program and an external source. The traditional evaluation algorithm for hex-programs is based on guessing truth values of external atoms and verifying them by explicit calls of the external source. The approach was optimized by techniques that reduce the number of necessary verification calls or speed them up, but the remaining external calls are still expensive. In this paper, we present an alternative evaluation approach based on inlining of external atoms, motivated by existing but less general approaches for specialized formalisms such as DL-programs. External atoms are then compiled away such that no verification calls are necessary. The approach is implemented in the dlvhex reasoner. Experiments show a significant performance gain. Besides performance improvements, we further exploit inlining for extending previous (semantic) characterizations of program equivalence from ASP to hex-programs, including those of strong equivalence, uniform equivalence, and $\langle\mathcal{H},\mathcal{B}\rangle$- equivalence. Finally, based on these equivalence criteria, we characterize also inconsistency of programs w.r.t. extensions. Since well-known ASP extensions (such as constraint ASP) are special cases of hex, the results are interesting beyond the particular formalism.

Exploiting Partial Assignments for Efficient Evaluation of Answer Set Programs with External Source Access

Answer Set Programming (ASP) is a well-known declarative problem solving approach based on nonmonotonic logic programs, which has been successfully applied to a wide range of applications in artificial intelligence and beyond. To address the needs of modern applications, HEX-programs were introduced as an extension of ASP with external atoms for accessing information outside programs via an API style bi-directional interface mechanism. To evaluate such programs, conflict-driving learning algorithms for SAT and ASP solving have been extended in order to capture the semantics of external atoms. However, a drawback of the state-of-the-art approach is that external atoms are only evaluated under complete assignments (i.e., input to the external source) while in practice, their values often can be determined already based on partial assignments alone (i.e., from incomplete input to the external source). This prevents early backtracking in case of conflicts, and hinders more efficient evaluation of HEX-programs. We thus extend the notion of external atoms to allow for three-valued evaluation under partial assignments, while the two-valued semantics of the overall HEX-formalism remains unchanged. This paves the way for three enhancements: first, to evaluate external sources at any point during model search, which can trigger learning knowledge about the source behavior and/or early backtracking in the spirit of theory propagation in SAT modulo theories (SMT). Second, to optimize the knowledge learned in terms of so-called nogoods, which roughly speaking are impossible input-output configurations. Shrinking nogoods to their relevant input part leads to more effective search space pruning. And third, to make a necessary minimality check of candidate answer sets more efficient by exploiting early external evaluation calls. As this check usually accounts for a large share of the total runtime, optimization is here particularly important. We further present an experimental evaluation of an implementation of a novel HEX-algorithm that incorporates these enhancements using a benchmark suite. Our results demonstrate a clear efficiency gain over the state-of-the-art HEX-solver for the benchmarks, and provide insights regarding the most effective combinations of solver configurations.