625 research outputs found

    Constructing Conditional Plans by a Theorem-Prover

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    The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system. This setting raises the questions of how to represent the plans and how to perform plan search. The answers are quite different from those in the simpler classical framework. In this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning. Translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations. Instead, we translate conditional planning to quantified Boolean formulae. We discuss three formalizations of conditional planning as quantified Boolean formulae, and present experimental results obtained with a theorem-prover

    Planning with Incomplete Information

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    Planning is a natural domain of application for frameworks of reasoning about actions and change. In this paper we study how one such framework, the Language E, can form the basis for planning under (possibly) incomplete information. We define two types of plans: weak and safe plans, and propose a planner, called the E-Planner, which is often able to extend an initial weak plan into a safe plan even though the (explicit) information available is incomplete, e.g. for cases where the initial state is not completely known. The E-Planner is based upon a reformulation of the Language E in argumentation terms and a natural proof theory resulting from the reformulation. It uses an extension of this proof theory by means of abduction for the generation of plans and adopts argumentation-based techniques for extending weak plans into safe plans. We provide representative examples illustrating the behaviour of the E-Planner, in particular for cases where the status of fluents is incompletely known.Comment: Proceedings of the 8th International Workshop on Non-Monotonic Reasoning, April 9-11, 2000, Breckenridge, Colorad

    A Divergence Critic for Inductive Proof

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    Inductive theorem provers often diverge. This paper describes a simple critic, a computer program which monitors the construction of inductive proofs attempting to identify diverging proof attempts. Divergence is recognized by means of a ``difference matching'' procedure. The critic then proposes lemmas and generalizations which ``ripple'' these differences away so that the proof can go through without divergence. The critic enables the theorem prover Spike to prove many theorems completely automatically from the definitions alone.Comment: See http://www.jair.org/ for any accompanying file

    Automatic synthesis of decision procedures

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    Strategic Issues, Problems and Challenges in Inductive Theorem Proving

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    Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP

    Automatically Leveraging MapReduce Frameworks for Data-Intensive Applications

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    MapReduce is a popular programming paradigm for developing large-scale, data-intensive computation. Many frameworks that implement this paradigm have recently been developed. To leverage these frameworks, however, developers must become familiar with their APIs and rewrite existing code. Casper is a new tool that automatically translates sequential Java programs into the MapReduce paradigm. Casper identifies potential code fragments to rewrite and translates them in two steps: (1) Casper uses program synthesis to search for a program summary (i.e., a functional specification) of each code fragment. The summary is expressed using a high-level intermediate language resembling the MapReduce paradigm and verified to be semantically equivalent to the original using a theorem prover. (2) Casper generates executable code from the summary, using either the Hadoop, Spark, or Flink API. We evaluated Casper by automatically converting real-world, sequential Java benchmarks to MapReduce. The resulting benchmarks perform up to 48.2x faster compared to the original.Comment: 12 pages, additional 4 pages of references and appendi

    Deductive synthesis of recursive plans in linear logic

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    Centre for Intelligent Systems and their ApplicationsConventionally, the problem of plan formation in Artificial Intelligence deals with the generation of plans in the form of a sequence of actions. This thesis describes an approach to extending the expressiveness of plans to include conditional branches and recursion. This allows problems to be solved at a higher level, such that a single plan in such a language is capable of solving a class of problems rather than a single problem instance. A plan of fixed size may solve arbitrarily large problem instances. To form such plans, we take a deductive planning approach, in which the formation of the plan goes hand-in-hand with the construction of the proof that the plan specification is realisable. The formalism used here for specifying and reasoning with planning problems is Girard's Institutionistic Linear Logic (ILL), which is attractive for planning problems because state change can be expressed directly as linear implication, with no need for frame axioms. We extract plans by means of the relationship between proofs in ILL and programs in the style of Abramsky. We extend the ILL proof rules to account for induction over inductively defined types, thereby allowing recursive plans to be synthesised. We also adapt Abramsky's framework to partially evaluate and execute the plans in the extended language. We give a proof search algorithm tailored towards the fragment of the ILL employed (excluding induction rule selection). A system implementation, Lino, comprises modules for proof checking, automated proof search, plan extraction and partial evaluation of plans. We demonstrate the encodings and solutions in our framework of various planning domains involving recursion. We compare the capabilities of our approach with the previous approaches of Manna and Waldinger, Ghassem-Sani and Steel, and Stephen and Biundo. We claim that our approach gives a good balance between coverage of problems that can be described and the tractability of proof search
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