Inductive Inference with Additional Information

AbstractWe consider the problem of inductively inferring a grammar for a language, given (positive) examples of the language and putative (possibly faulty) grammars for the complement of the language. The criterion of success is identification in the limit, defined by E. M. Gold (1967, Inform. and Control10, 447–474). Additional information is useful insofar as it allows the identification of language classes that would not be identified with positive examples alone. An infinite sequence of grammars past some finite position are correct for the complement of the input language, is not as useful a form of additional information as a single correct grammar for the complement. Grammars that are almost correct for the complement (that is, that make finitely many errors) are not as useful as correct grammars, and the usefulness of a grammar decreases with increasing numbers of errors

Deep Ecology in William Gilpin\u27s Sermons

Deep Ecology seeks to minimize or erase human impact on the natural world. As a homilist, the eighteenth-century picturesque travel-writer, philosopher, and cleric William Gilpin provides insights that accord with and complicate our understanding of Deep Ecology. His role as an Anglican cleric is mostly forgotten, although his collected religious works comprise four volumes and also build on, define, and problematize the aesthetics he develops in his other works. If the major tenet of the Deep Ecology movement is the erasure or minimalizing of the human, Gilpin’s practice as a pastor and his depiction of Christians on their journeys of faith downplays human agency, replacing it with a connection to the world of nature and the divine. His own practice as a homily writer, as told to younger men seeking to pursue a life in the church and related in the Preface to his first collection of sermons, was to take with him “a memorandum book” and “a text or two of scripture” as he “walked about his parish, and afterwards when he was able onto to walk into his garden and fields” (1.x). The natural world and the rhythms of nature and town form a key part of Gilpin’s meditation, leading him to diminish humankind’s impact on the world around them. My paper will examine the multiple ways that Gilpin’s love of the natural world expressed through his sermons becomes a precursor to the Deep Ecology movement and further complicates our understanding of our stewardship of the natural world

Open Problems in Systems that Learn

In this paper we give solutions to some of the open problems in [OSW86]. We also give partial solutions to the other open problems

Approximate Inference and Scientific Method 1

CCR 8320136 to the University of Rochester. A new identification criterion, motivated by notions of successively improving approximations in the philosophy of science, is defined. It is shown that the class of recursive functions is identifiable under this criterion. This result is extended to permit somewhat more realistic types of data than usual. This criterion is then modified to consider restrictions on the quality of approximations, and the new criteria are compared to existing criteria.

Approximate inference and scientific method

A new identification criterion, motivated by notions of successively improving approximations in the philosophy of science, is defined. It is shown that the class of recursive functions is identifiable under this criterion. This result is extended to permit somewhat more realistic types of data than usual. This criterion is then modified to consider restrictions on the quality of approximations

Learning in the Presence of Inaccurate Information

In this paper we discuss the effects of errors in input data on recursion theoretic learning. We consider three types of inaccuracy in input data depending on the presence of extra data (noise), missing data (incompleteness) or both (imperfection). We show that for function learning incompleteness harms strictly more than noise. However for language learning, identification on incomplete text and identification on noisy text are incomparable. We also prove hierarchies based on the number of inaccuracies present in the input

Efficient Language Instance Generation

For many familiar languages in P or NP, such as the set of connected graphs or the set of satisfiable CNF boolean formulas, it appears easy to determine whether there exist any instances in the language having a certain size, and even to construct an instance of the desired size on demand. With a little more thought one can also come up with polynomial time nondeterministic or probabilistic procedures which can output all instances of the language of a given size, albeit with repetitions and not necessarily in a uniform manner. In this paper we investigate whether such efficient procedures exist for all languages in P or NP. We exhibit relativizations which show that this question cannot be easily answered. We also relate construction, generation, and categorical generation (generation with unique computation path for each string generated, i.e. no repetitions), to the existence of sparse languages in NP-P and in Dp-P. We give a characterization of the languages in NP which can be efficiently constructed from which it can be deduced that all languages in NP can be efficiently constructed if and only if all languages in P can be efficiently constructed. We also deal with parameter-based generation, with construction in the polynomial time hierarchy, and with the existence of certain types of generators viewed as NP machines