Efficient Automated Planning with New Formulations

Problem solving usually strongly relies on how the problem is formulated. This fact also applies to automated planning, a key field in artificial intelligence research. Classical planning used to be dominated by STRIPS formulation, a simple model based on propositional logic. In the recently introduced SAS+ formulation, the multi-valued variables naturally depict certain invariants that are missed in STRIPS, make SAS+ have many favorable features. Because of its rich structural information SAS+ begins to attract lots of research interest. Existing works, however, are mostly limited to one single thing: to improve heuristic functions. This is in sharp contrast with the abundance of planning models and techniques in the field. On the other hand, although heuristic is a key part for search, its effectiveness is limited. Recent investigations have shown that even if we have almost perfect heuristics, the number of states to visit is still exponential. Therefore, there is a barrier between the nice features of SAS+ and its applications in planning algorithms. In this dissertation, we have recasted two major planning paradigms: state space search and planning as Satisfiability: SAT), with three major contributions. First, we have utilized SAS+ for a new hierarchical state space search model by taking advantage of the decomposable structure within SAS+. This algorithm can greatly reduce the time complexity for planning. Second, planning as Satisfiability is a major planning approach, but it is traditionally based on STRIPS. We have developed a new SAS+ based SAT encoding scheme: SASE) for planning. The state space modeled by SASE shows a decomposable structure with certain components independent to others, showing promising structure that STRIPS based encoding does not have. Third, the expressiveness of planning is important for real world scenarios, thus we have also extended the planning as SAT to temporally expressive planning and planning with action costs, two advanced features beyond classical planning. The resulting planner is competitive to state-of-the-art planners, in terms of both quality and performance. Overall, our work strongly suggests a shifting trend of planning from STRIPS to SAS+, and shows the power of formulating planning problems as Satisfiability. Given the important roles of both classical planning and temporal planning, our work will inspire new developments in other advanced planning problem domains

Resolution Proof Technique in Linear Temporal Logic.

This dissertation presents a resolution proof technique for Propositional Linear Temporal Logic of discrete time with the Until operator. The presented proof technique stems from the resolution method developed by L. Farinas del Cerro and A. Cavalli. However, their method is incomplete, and their completeness proof, as originally reported, is incorrect. Unlike Farinas\u27s method, our proof technique incorporated the Until operator, which is a very powerful and useful in describing complex temporal relationships which are common in many areas of computer science. Our technique is also proved complete. The presented resolution method for linear temporal logic is similar to classical resolutions: the main goal is to show unsatisfiability of a set of temporal clauses by locating, either directly or indirectly, a state which contains unsatisfiability. Subsequent resolvents of a refutation are obtained by resolving out complementary literals referring to the same instant of time. In order to increase the efficiency of the resolution proof technique, we have developed a refinement of the presented basic method. This refinement is similar to the well-known Ordered Linear (OL) strategy for classical resolution. We also present the lifting of the basic resolution method to predicate linear temporal logic. Unlike First Order Logic, clauses of predicate linear temporal logic may contain variables which are quantified existentially, because skolemization is not valid here. We use standard unification with substitution on universally quantified variables. However, if a term substituted in place of a variable contains any flexible symbols, a constant or a function is flexible if it has different translation in different states, then all occurrences of the substituted variable must refer to the same instant of time (state). Otherwise, the unification may lead to incorrect results. Resolution in predicate linear temporal logic, though very useful from a practical standpoint, is incomplete, since no predicate temporal logic with arithmetic model of time is complete

Commonsense Metaphysics and Lexical Semantics

In the TACITUS project for using commonsense knowledge in the understanding of texts about mechanical devices and their failures, we have been developing various commonsense theories that are needed to mediate between the way we talk about the behavior of such devices and causal models of their operation. Of central importance in this effort is the axiomatization of what might be called commonsense metaphysics. This includes a number of areas that figure in virtually every domain of discourse, such as granularity, scales, time, space, material, physical objects, shape, causality, functionality, and force. Our effort has been to construct core theories of each of these areas, and then to define, or at least characterize, a large number of lexical items in terms provided by the core theories. In this paper we discuss our methodological principles and describe the key ideas in the various domains we are investigating

An analysis and implementation of linear derivation strategies

This study examines the efficacy of six linear derivation strategies: (i) s-linear resolution, (ii) the ME procedure; (iii) t-linear resolution, (iv) SL -resolution, (v) the GC procedure, and (vi) SLM. The analysis is focused on the different restrictions and operations employed in each derivation strategy. The selection function, restrictive ancestor resolution, compulsory ancestor resolution on literals having atoms which are or become identical, compulsory merging operations, reuse of truncated literals, spreading of FALSE literals, no-tautologies resection, no two non-B-literals having identical atoms restriction, and the use of semantic information to trim irrelevant derivations from the search tree are the major features found In these six derivation strategies. Detecting loops and minimizing irrelevant derivations are the identified weak points of SLM. Two variations of SLM are suggested to rectify these problems. The ME procedure, SL-resolution, the GC procedure, SLM and one of the suggested variations of SLM were implemented using the Arity/Prolog compiler to produce the ME -TP, SL-TP, GC-TP, SLM-TP and SLM5-TP theorem provers respectively. In addition to the original features of each derivation strategy, the following search strategies were included in the implementations : the modified consecutively bounded depth-first search unit preference strategy, set of support strategy, pure literal elimination, tautologous clause elimination, selection function based on the computed weight of a literal, and a match check. The extension operation used by each theorem prover was extended to include subsumed unit extension and paramodulation. The performance of each theorem prover was determined. Experimental results were obtained using twenty four selected problems. The performance was measured in terms of the memory use and the execution time. A comparison of results between the five theorem provers using the, ME-TP as the basis was done. The results show that none of the theorem provers, consistently perform better than the others. Two of the selected problems were not proved by SL-TP and one problem was not proved by SLM-TP due to memory problems. The ME-TP, GC-TP and SLM5-TP proved all the selected problems. In some problems, the ME-TP and GC-TP performed better than SLM5-TP. However, the ME-TP and GC-TP had difficulties in some problems in which SLM5-TP performed well

Subsumption in Modal Logic

Subsumption has long been known as a technique to detect redundant clauses in the search space of automated deduction systems for classical first order logic. In recent years several automated deduction methods for non-classical modal logics have been developed. This thesis explores, how subsumption can be made to work in the context of these modal logic deduction methods. Many modern modal logic deduction methods follow an indirect approach. They translate the modal sentences into some other target language, and then determine whether there exists a proof in that language, rather than doing deduction in the modal language itself. Consequently, subsumption then needs to focus on the target language, in which the actual proof is done. World Path Logic (WPL) is introduced as a possible target language. Deduction in WPL works very much like in ordinary logic, the only significant difference is the need for a special purpose unification, which unifies world paths under an equational theory (E-unification). Relating WPL to a well understood first order logic of restricted quantification, the properties of WPL, that make deduction work, are examined. The obtained theoretical results are the basis for the following treatment of subsumption in WPL. Subsumption is analyzed treating a clause as a scheme standing for the set of its ground instances. Although the notion of ground instances in WPL is different from ordinary logic, it turns out that - just like in ordinary logic - a clause Cl subsumes another clause C2, if there exists a substitution 6 such that C10 £ C2. Once the special purpose unification has been implemented into a theorem prover to allow for deduction in WPL, existing subsumption tests then work without any further changes

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

The role of the crucial experiment in student modelling

As the range of models which tutoring systems can capture is extended, efficient diagnosis becomes more difficult. This thesis describes a solution to this problem based on the generation of 'Critical Problems'; their role in student modelling is analogous to that of the 'Crucial Experiment' in science. We argue that great diagnostic power can be obtained by generating discriminatory problem examples. In general, efficient diagnosis is just not possible without such an hypothesis-testing capability. We describe a program, PO, which given a pair of production rule models and a description of the class of problems which the student must solve, generates an abstract specification of the problems which discriminate between those two hypotheses. Through a process termed 'Abstract Interpretation', PO tips the balance in favour of diagnostic measurement. The key to this problem lies in the realisation that we are only interested in the abstract mapping between a model's inputs and outputs; from the point of view of generating a Critical Problem, the intermediate processing of the model is irrelevant

Resolution-based methods for linear temporal reasoning

The aim of this thesis is to explore the potential of resolution-based methods for linear temporal reasoning. On the abstract level, this means to develop new algorithms for automated reasoning about properties of systems which evolve in time. More concretely, we will: 1) show how to adapt the superposition framework to proving theorems in propositional Linear Temporal Logic (LTL), 2) use a connection between superposition and the CDCL calculus of modern SAT solvers to come up with an efficient LTL prover, 3) specialize the previous to reachability properties and discover a close connection to Property Directed Reachability (PDR), an algorithm recently developed for model checking of hardware circuits, 4) further improve PDR by providing a new technique for enhancing clause propagation phase of the algorithm, and 5) adapt PDR to automated planning by replacing the SAT solver inside with a planning-specific procedure. We implemented the proposed ideas and provide experimental results which demonstrate their practical potential on representative benchmark sets. Our system LS4 is shown to be the strongest LTL prover currently publicly available. The mentioned enhancement of PDR substantially improves the performance of our implementation of the algorithm for hardware model checking in the multi-property setting. It is expected that other implementations would benefit from it in an analogous way. Finally, our planner PDRplan has been compared with the state-of-the-art planners on the benchmarks from the International Planning Competition with very promising results.Das Ziel dieser Doktorarbeit ist es, das Potential resolutionsbasierter Methoden zur linearer, temporaler Beweisführung zu untersuchen. Von einem abstrakten Gesichtspunkt aus gesehen bedeutet dies, neue Algorithmen über die Eigenschaften von sich zeitlich entwicklenden Systemen im Bereich des automatischen Theorembeweisens zu entwickeln. Konkreter gesagt werden wir 1) aufzeigen, wie sich das Rahmenprogramm der Superposition so anpassen lässt, damit es Theoreme in propositionaler Linear Temporal Logic (LTL) beweist, 2) eine Verbindung zwischen der Superposition und dem CDCL-Kalkül moderner SAT-Solver nutzen, um mit einem effizienten LTL-Prover aufzuwarten, 3) das Vorangegangene auf Erreichbarkeitseigenschaften spezialisieren, und eine starke Verbindung zu der Property Directed Reachability (PDR), einem jüngst eintwickeltem Model-Checking-Algorithmus für Hardware-Schaltkreise, aufzudecken, 4) PDR durch die Einführung neuer Technik verbessern, die die Clause-Propagation-Phase des Algorithmus beschleunigt, und 5) PDR für das automatisierte Planen anpassen, indem wir den inneren SAT-Solver durch eine planungsspezifische Prozedur ersetzen. Wir haben die vorgeschlagenen Ideen implementiert, und es werden experimentelle Ergebnisse angegeben, die das praktische Potential dieser Ideen auf repräsentativen Benchmarks aufzeigt. Es hat sich herausgestellt, dass unser System LS4 der staerkste öffentlich zugängliche LTL-Prover ist. Die erwähnte Erweiterung von PDR verbessern die Leistungsfähigkeit unserer Implementierung des Hardware-Model-Checking-Algorithmus substantiell im Bereich der Multi-Property-Einstellungen. Wir erwarten, dass andere Implementierungen in ähnlicher Weise profitieren würden. Schließlich haben wir viel versprechende Ergebnisse durch den Vergleich unser Planer PDRplan mit anderen state-of-the-art Planer auf den Benchmarks der International Planning Competition erzielt

Assertion level proof planning with compiled strategies

This book presents new techniques that allow the automatic verification and generation of abstract human-style proofs. The core of this approach builds an efficient calculus that works directly by applying definitions, theorems, and axioms, which reduces the size of the underlying proof object by a factor of ten. The calculus is extended by the deep inference paradigm which allows the application of inference rules at arbitrary depth inside logical expressions and provides new proofs that are exponentially shorter and not available in the sequent calculus without cut. In addition, a strategy language for abstract underspecified declarative proof patterns is developed. Together, the complementary methods provide a framework to automate declarative proofs. The benefits of the techniques are illustrated by practical applications.Die vorliegende Arbeit beschäftigt sich damit, das Formalisieren von Beweisen zu vereinfachen, indem Methoden entwickelt werden, um informale Beweise formal zu verifizieren und erzeugen zu können. Dazu wird ein abstrakter Kalkül entwickelt, der direkt auf der Faktenebene arbeitet, welche von Menschen geführten Beweisen relativ nahe kommt. Anhand einer Fallstudie wird gezeigt, dass die abstrakte Beweisführung auf der Fakteneben vorteilhaft für automatische Suchverfahren ist. Zusätzlich wird eine Strategiesprache entwickelt, die es erlaubt, unterspezifizierte Beweismuster innerhalb des Beweisdokumentes zu spezifizieren und Beweisskizzen automatisch zu verfeinern. Fallstudien zeigen, dass komplexe Beweismuster kompakt in der entwickelten Strategiesprache spezifiziert werden können. Zusammen bilden die einander ergänzenden Methoden den Rahmen zur Automatisierung von deklarativen Beweisen auf der Faktenebene, die bisher überwiegend manuell entwickelt werden mussten