Hybrid ASP

This paper introduces an extension of Answer Set Programming (ASP) called Hybrid ASP which will allow the user to reason about dynamical systems that exhibit both discrete and continuous aspects. The unique feature of Hybrid ASP is that it allows the use of ASP type rules as controls for when to apply algorithms to advance the system to the next position. That is, if the prerequisites of a rule are satisfied and the constraints of the rule are not violated, then the algorithm associated with the rule is invoked

Delayed predicate algorithm evaluation in hybrid answer set programming (ASP)

A hybrid answer set programming (ASP) solver is a logic programming type solver with a variety of applications, e.g., diagnosing software failures, modeling dynamical systems, etc. A hybrid ASP solver finds solutions for hybrid ASP programs, which are sets of hybrid ASP rules. Hybrid ASP rules include stationary rules with associated predicate algorithms and advancing rules with associated advancing algorithms. Solutions to hybrid ASP programs are found iteratively by starting with an initial state and producing consequent states. Part of computing a consequent state involves determination of the stationary rules that are applicable at the consequent state. This in turn involves evaluating predicate algorithms associated with the rules. This approach is inefficient, since it requires that all the predicate algorithms be evaluated in all the states. The techniques of this disclosure avoid the inefficiency of evaluating predicate algorithms by adding auxiliary rules that enable intelligent guesses as to whether an algorithm will accept or reject, in turn enabling the continued evaluation of the rules without the evaluation of the algorithms

Hybrid ASP-based Approach to Pattern Mining

Detecting small sets of relevant patterns from a given dataset is a central challenge in data mining. The relevance of a pattern is based on user-provided criteria; typically, all patterns that satisfy certain criteria are considered relevant. Rule-based languages like Answer Set Programming (ASP) seem well-suited for specifying such criteria in a form of constraints. Although progress has been made, on the one hand, on solving individual mining problems and, on the other hand, developing generic mining systems, the existing methods either focus on scalability or on generality. In this paper we make steps towards combining local (frequency, size, cost) and global (various condensed representations like maximal, closed, skyline) constraints in a generic and efficient way. We present a hybrid approach for itemset, sequence and graph mining which exploits dedicated highly optimized mining systems to detect frequent patterns and then filters the results using declarative ASP. To further demonstrate the generic nature of our hybrid framework we apply it to a problem of approximately tiling a database. Experiments on real-world datasets show the effectiveness of the proposed method and computational gains for itemset, sequence and graph mining, as well as approximate tiling. Under consideration in Theory and Practice of Logic Programming (TPLP).Comment: 29 pages, 7 figures, 5 table

On the semantics of hybrid ASP systems based on Clingo

[Abstract]: Over the last decades, the development of Answer Set Programming (ASP) has brought about an expressive modeling language powered by highly performant systems. At the same time, it gets more and more difficult to provide semantic underpinnings capturing the resulting constructs and inferences. This is even more severe when it comes to hybrid ASP languages and systems that are often needed to handle real-world applications. We address this challenge and introduce the concept of abstract and structured theories that allow us to formally elaborate upon their integration with ASP. We then use this concept to make the semantic characterization of clingo’s theory-reasoning framework precise. This provides us with a formal framework in which we can elaborate upon the formal properties of existing hybridizations of clingo, such as clingcon, clingo[dl], and clingo[lp].This work was supported by DFG grant SCHA 550/11, Germany, by grant PID2020-116201GB-I00 funded by MCIN/AEI/ 10.13039/501100011033, Spain, by Xunta de Galicia and the European Union, GPC ED431B 2022/33, by European COST action CA17124 DigForASP, EU, and by the National Science Foundation (NSF 95-3101-0060-402), USA.Xunta de Galicia; ED431B 2022/33Deutsche Forschungsgemeinschaft; SCHA 550/11United States. National Science Foundation; NSF 95-3101-0060-40

Hybrid ASP-based multi-objective scheduling of semiconductor manufacturing processes (Extended version)

Modern semiconductor manufacturing involves intricate production processes consisting of hundreds of operations, which can take several months from lot release to completion. The high-tech machines used in these processes are diverse, operate on individual wafers, lots, or batches in multiple stages, and necessitate product-specific setups and specialized maintenance procedures. This situation is different from traditional job-shop scheduling scenarios, which have less complex production processes and machines, and mainly focus on solving highly combinatorial but abstract scheduling problems. In this work, we address the scheduling of realistic semiconductor manufacturing processes by modeling their specific requirements using hybrid Answer Set Programming with difference logic, incorporating flexible machine processing, setup, batching and maintenance operations. Unlike existing methods that schedule semiconductor manufacturing processes locally with greedy heuristics or by independently optimizing specific machine group allocations, we examine the potentials of large-scale scheduling subject to multiple optimization objectives.Comment: 17 pages, 1 figure, 4 listings, 1 table; a short version of this paper is presented at the 18th European Conference on Logics in Artificial Intelligence (JELIA 2023