The CADE-14 ATP System Competition

This paper documents the design, competing systems, results, and conclusions of the CADE-14 ATP System Competition (CASC-14).     

广义Foster定理

利用Ｍａｘｗｅｌｌ方程组导出了适用于有耗网络的广义Ｆｏｓｔｅｒ定理，得到了一些有关电抗斜率以及Ｑ值的有用公式及结论。     

Implicit induction in conditional theories

We propose a new procedure for proof by induction in conditional theories where case analysis is simulated by term rewriting. This technique reduces considerably the number of variables of a conjecture to be considered for applying induction schemes. Our procedure is presented as a set of inference rules whose correctness has been formally proved. Moreover, when the axioms are ground convergent and the functions are completely defined, it is possible to apply the system for refuting conjectures. The procedure is even refutationally complete for conditional equations with Boolean preconditions over free constructors. The method is entirely implemented in the proverSPIKE. This system has solved interesting problems in a completely automatic way, that is, without interaction with the user and without ad hoc heuristics. It has also proved the challenging Gilbreath card trick, with only two easy lemmas.Preliminary versions of the results have been presented at the 13th International Joint Conference on Artificial Intelligence, Chambéry (France), 1993 (Bouhoula and Rusinowith, 1993).     

A λ-unifiability test for set theory

We present a semi-decision algorithm for the unifiability of two set-theoretic formulas modulo -reduction. The algorithm is based on the approach developed by G. Huet for type theory, but requires additional measures because formulas in set theory are not all normalizable. We present the algorithm in an Ada-like pseudocode, and then prove two theorems that show the completeness and correctness of the procedure. We conclude by showing that -unification is not a complete quantifier substitution method for set theory-unlile first-order unification and first-order logic. In this respect set theory is similar to type theory (higher-order logic).This material is based upon work supported by the National Science Foundation under award number ISI-8560438. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation.     

Higher-Order and Modal Logic as a Framework for Explanation-Based Generalization

Certain tasks, such as formal program development and theorem proving, fundamentally rely upon the manipulation of higher-order objects such as functions and predicates. Computing tools intended to assist in performing these tasks are at present inadequate in both the amount of knowledge they contain (i.e., the level of support they provide) and in their ability to learn (i.e., their capacity to enhance that support over time). The application of a relevant machine learning technique—explanation-based generalization (EBG)—has thus far been limited to first-order problem representations. We extend EBG to generalize higher-order values, thereby enabling its application to higher-order problem encodings.Logic programming provides a uniform framework in which all aspects of explanation-based generalization and learning may be defined and carried out. First-order Horn logics (e.g., Prolog) are not, however, well suited to higher-order applications. Instead, we employ Prolog, a higher-order logic programming language, as our basic framework for realizing higher-order EBG. In order to capture the distinction between domain theory and training instance upon which EBG relies, we extend Prolog with the necessity operator of modal logic. We develop a meta-interpreter realizing EBG for the extended language, Prolog, and provide examples of higher-order EBG.     

Modal logic as metalogic

The goal of this paper is to show how modal logic may be conceived as recording the derived rules of a logical system in the system itself. This conception of modal logic was propounded by Dana Scott in the early seventies. Here, similar ideas are pursued in a context less classical than Scott's.First a family of propositional logical systems is considered, which is obtained by gradually adding structural rules to a variant of the nonassociative Lambek calculus. In this family one finds systems that correspond to the associative Lambek calculus, linear logic, relevant logics, BCK logic and intuitionistic logic. Above these basic systems, sequent systems parallel to the basic systems are constructed, which formalize various notions of derived rules for the basic systems. The deduction theorem is provable for the basic systems if, and only if, they are at least as strong as systems corresponding to linear logic, or BCK logic, depending on the language, and their deductive metalogic is not stronger than they are.However, though we do not always have the deduction theorem, we may always obtain a modal analogue of the deduction theorem for conservative modal extensions of the basic systems. Modal postulates which are necessary and sufficient for that are postulates of S4 plus modal postulates which mimic structural rules. For example, the modal postulates which Girard has recently considered in linear logic are necessary and sufficient for the modal analogue of the deduction theorem.All this may lead towards results about functional completeness in categories. When functional completeness, which is analogous to the deduction theorem, fails, we may perhaps envisage a modal analogue of functional completeness in a modal category, of which our original category is a full subcategory.     

Fuzzy度量空间上映射的又一个不动点定理

继文献〔1〕之后证明了Fuzzy度量空间上映射的又一个不动点定理，使文献〔2〕的§1（3，4）的定理成为本文的特例。     

HIGHER ORDER MOMENTS OF SAMPLE AUTOCOVARIANCES AND SAMPLE AUTOCORRELATIONS FROM AN INDEPENDENT TIME SERIES

Abstract. Given length- n sampled time series, generated by an independent distributed process, in this paper we treat the problem of determining the greatest order, in n , that moments of the sample autocovariances and sample autocorrelations can attain. For the sample autocovariance moments, we achieve quite general results; but, for the autocorrelation moments, we restrict study to Gaussian white noise (normal, independent and identically distributed). Our main theorem relates to the cross-moments of the non-centred sample autocovariances, but we also establish a relation between these and the corresponding moments for the centred sample autocovariances.     

AN ITERATIVE FILTERING ALGORITHM FOR NON-FOURIER FREQUENCY ESTIMATION

Abstract. We study an iterative filtering method to estimate frequencies of random Gaussian sinusoids in white noise. The method uses higher order crossings and takes advantage of a fixed point to guide the use of bandpass filtering in an attempt effectively to increase the signal-to-noise ratio. At each iteration the expected zero-crossing rate is estimated from independent time series. Convergence occurs with any prespecified probability less than one.     

分布式非线性控制的回路小增益方法

近年来,分布式控制在控制及相关学科引起了广泛的兴趣.复杂的包含不确定性的非线性动力学在控制系统中普遍存在,而针对这种系统的分布式控制研究尚处于起步阶段.其中一个关键问题就是由分布式控制系统中信息交换约束与复杂非线性动力学的并存所导致的.近期相关研究表明,基于回路小增益定理的控制设计方法能够较有效地解决这类问题.本文重点回顾分布式控制回路小增益方法的近期主要结果,给出了一种分布式非线性控制器的系统化设计方法,并在此基础上指出若干未来研究方向.