Recently, rich subclasses of elementary formal systems (EFS) have been shown to be identifiable in the limit from only positive data. Examples of these classes are Angluin’s pattern languages, unions of pattern languages by Wright and Shinohara, and classes of languages definable by length-bounded elementary formal systems studied by Shinohara. The present paper employs two distinct bodies of abstract studies in the inductive inference literature to analyze the learnability of these concrete classes. The first approach, introduced by Freivalds and Smith, uses constructive ordinals to bound the number of mind changes. ω denotes the first limit ordinal. An ordinal mind change bound of ω means that identification can be carried out by a learner that after examining some element(s) of the language announces an upper bound on the number of mind changes it will make before converging; a bound of ω · 2 means that the learner reserves the right to revise this upper bound once; a bound of ω · 3 means the learner reserves the right to revise this upper bound twice, and so on. A bound of ω 2 means that identification can be carried out by a learner that announces an upper bound on the number of times it may revise its conjectured upper bound on the number of mind changes. It is shown in the present paper that the ordinal mind change complexity for identification of languages formed by unions of up to n pattern languages is ω n. It is

An elementary formal system (EFS , for short) is a kind of logic program which directly manipulates character strings. A number of researches have investigated the ability of EFS as an uniform framework for language learning in various learning models including model inference, inductive inference, and PAC-learning. In this paper, we investigate the polynomial time learnability of EFS from the view of active learning allowing membership queries. Positive results include the polynomial time learnability of the class of terminating HEFS of variable-occurrence k and arity r from equivalence queries and entailment membership queries with the information on termination. We also presented a lower bound result showing that the algorithm is near optimal in the query complexity. Negative results include a series of representation-independent hardness results, which fill the gap between the learnable and the non-learnable subclasses of EFS in our knowledge. Particularly, we showed th...

The inverse resolution(IR for short) is a procedure to produce new clauses by applying the resolution principle in the opposite direction. It has mainly been studied in terms of logic. The elementary formal systems(EFSs for short) invented by Smullyan have been proved suitable for formal language learning as a unified framework. In this paper we consider the problem of learning EFS languages from positive examples by applying IR in EFS framework. First, we give a realization of IR in EFS. Based on the realization, we try to give an efficient learning procedure for an EFS language class, which is a subclass of regular languages, from positive examples. Key words: machine learning, logic program, inverse resolution, EFS, formal language learning 1 INTRODUCTION Inductive learning is mainly studied in the context of logics and formal languages. A lot of learning methods have been discovered in the field of inductive logic programming[9]. One of the main techniques proposed by Muggleton[...

In this paper we present the class of general logic programs which has a special kind of stratifications, called the locally finite stratification. For the class, good properties of propositional logic programs, such as termination and safeness, are preserved. Using these properties, we show the completeness of a kind of SLDNF-resolution that use a depth bound, called depth bounded resolution, with respect to the perfect model semantics. Finally we syntactically characterize a subclass of the class, called weakly reducing programs and show that the depth bounded resolution is complete and effective for weakly reducing programs. 1 Introduction The completeness of a derivation procedure with respect to the perfect model semantics is important in both logic programming and non-monotonic reasoning. Perfect model semantics were introduced by Przymisinski [13], Apt, Blair and Walker [3] and by Van Gelder [23] as the declarative semantics for the class of stratified logic programs [3, 23] a...

An elementary formal system (EFS) is a logic program such as a Prolog program, for instance, that directly manipulates strings. Arikawa and his co-workers proposed elementary formal systems as a unifying framework for formal language learning.

An elementary formal system (EFS) is a logic program such as a Prolog program, for instance, that directly manipulates strings.