. This paper presents techniques to guide equational reasoning in a goal directed way. Suggested by rippling methods developed in the field of inductive theorem proving we use annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function symbols we define different abstractions of formulas which are used for planning of proofs. Rippling techniques are used to refine single planning steps, e.g. the application of a bridge lemma, on a next planning level. Fachbeitrag. Keywords: Automated reasoning, Theorem Proving, Rippling 1 Introduction Heuristics for judging similarities between formulas and subsequently reducing differences have been applied to automated deduction since the 1950s, when Newell, Shaw, and Simon built their first "logic machine" [NSS63]. Since the later 60s, a similar theme of difference identification and reduction appears in the field of resolution theorem proving [Mor69], [Dig85], [BS88]. Partial unifica...

Abstract 2 Most autonomous agents are situated in a social context and need to interact with other agents (both human and artificial) to complete their problem solving objectives. Such agents are usually capable of performing a wide range of actions and engaging in a variety of social interactions. Faced with this variety of options, an agent must decide what to do. There are many potential decision making functions that could be employed to make the choice. Each such function will have a different effect on the success of the individual agent and of the overall system in which it is situated. To this end, this thesis examines agents ’ decision making functions to ascertain their likely properties and attributes. A novel framework for characterising social decision making is presented which provides explicit reasoning about the potential benefits of the individual agent, particular sub-groups of agents or the overall system. This framework enables multi-farious social interaction attitudes to be identified and defined; ranging from the purely self-interested to the purely altruistic. In particular, however, the focus is on the spectrum of socially responsible agent behaviours in which agents attempt to balance their own needs with those of the overall system. Such behaviour aims to ensure that both the agent and the overall system perform well.

In this paper we distinguish between two computational paradigms for knowledge discovery that share the notion of heuristic search, but dier in the importance they place on using scientific formalisms to state discovered knowledge. We also report progress on computational methods for discovering such communicable knowledge in two domains, one involving the regulation of photosynthesis in phytoplankton and the other involving carbon production by vegetation in the Earth ecosystem. In each case, we describe a representation for models, methods for using data to revise existing models, and some initial results. In closing, we discuss related work on the computational discovery of communicable scientific knowledge and outline directions for future research.

In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of its success on practical examples. For equality reasoning we use these annotated terms to represent syntactical differences of formulas. Based on these annotations and on hierarchies of function symbols we define different abstractions of formulas which are used for a hierarchical planning of proofs. Also rippling techniques are used to refine single planning steps, e.g. the application of a bridge lemma, on a next planning level. 1 Introduction In the field of inductive theorem proving syntactical differences between the induction hypothesis and induction conclusion are used in order to guide the proof [BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling ...

Flip-pushdown automata are pushdown automata with the additional ability to ip or reverse its pushdown. We investigate deterministic and nondeterministic ip-pushdown automata accepting by nal state or empty pushdown.

In this thesis we present new methods for the automated design of new heuristics in knowledge-lean applications and for finding heuristics that can be generalized to unlearned test cases. These applications lack domain knowledge for credit assignment; hence, operators for composing new heuristics are generally model free, domain independent, and syntactic in nature. The operators we have used are genetics based; examples of which include mutation and crossover. Learning is based on a generate-and-test paradigm that maintains a pool of competing heuristics, tests them to a limited extent, creates new ones from those that perform well in the past, and prunes poor ones from the pool. We have studied four important issues in learning better heuristics: (a) partitioning of a problem domain into smaller subsets, called subdomains, so that performance values within each subdomain can be evaluated statistically, (b) anomalies in performance evaluation within a subdomain, (c) rational scheduling of limited computational resources in testing candidate heuristics in single-objective as well as multi-objective learning, and (d) finding heuristics that can be generalized to unlearned subdomains. We show experimental results in learning better heuristics for (a) process placement for distributed-memory multicomputers, (b) node decomposition in a branch-and-bound search, (c) generation of test patterns in VLSI circuit testing, (d) VLSI cell placement and routing, and (e) blind equalization.

Introduction Heuristics are generally used in many real-world engineering applications ranging from computer aided design, optimization, scheduling and computer communications. Since the relationship between performance and control is unknown in heuristics, some parameters, functions, and procedures are designed either based on user experience or experimentally. These heuristics can usually be improved by automated tuning, machine learning, and generalization. In this chapter, we study the problem of performance generalization of the heuristics learned. 1.1 Terminologies We define a problem solver as an algorithm, or more generally, a software package used to solve a problem. A problem solver can be regarded as a black box, with some heuristic components or heuristics designed in an ad hoc way, where a heuristic is "A process that may solve a problem but offers no guarantees of doing so" 1 . Heu

We present a new approach to automated reasoning based on difference identification and reduction. Difference identification is based on a generalization of unification so that terms are made equal not only by finding substitutions for variables but also by hiding term structure. This annotation of structural differences serves to direct rippling, a type of rewriting designed to reduce and remove differences in a controlled way. On the technical side, we give a rule-based algorithm for difference unification, and analyze its correctness, completeness, and complexity. Moreover we show how it can be efficiently implemented based on a novel search strategy for unifiers. On the practical side, we show how this algorithm can be used in new ways to support and extend the role of rippling in theorem proving and other kinds of automated reasoning. 1 Introduction 1.1 Motivation and Background Heuristics for judging similarity between terms and subsequently reducing differences have been appli...

Flip-pushdown automata are pushdown automata with the additional power to ip or reverse its pushdown, and were recently introduced by Sarkar. We solve most of Sarkar's open problems. In particular, we show that k+1 pushdown reversals are better than k for both deterministic and nondeterministic ip-pushdown automata, i.e., there are languages which can be recognized by a deterministic ippushdown automaton with k + 1 pushdown reversals but which cannot be recognized by a k-ip-pushdown (deterministic or nondeterministic). Furthermore, we investigate closure and non-closure properties as well as computational complexity problems such as xed and general membership.

this paper, I will try to deal with the question of what concept of intelligence evolves from the work in AI. I will focus on two central paradigms that have found wide recognition, and I will keep short to point out their most significant points. Before doing so, I will give a brief historic account of the origins of the field of artificial intelligence.