A Logic For Inductive Probabilistic Reasoning

Inductive probabilistic reasoning is understood as the application of inference patterns that use statistical background information to assign (subjective) probabilities to single events. The simplest such inference pattern is direct inference: from “70% of As are Bs” and “a is an A” infer that a is a B with probability 0.7. Direct inference is generalized by Jeffrey’s rule and the principle of cross-entropy minimization. To adequately formalize inductive probabilistic reasoning is an interesting topic for artificial intelligence, as an autonomous system acting in a complex environment may have to base its actions on a probabilistic model of its environment, and the probabilities needed to form this model can often be obtained by combining statistical background information with particular observations made, i.e., by inductive probabilistic reasoning. In this paper a formal framework for inductive probabilistic reasoning is developed: syntactically it consists of an extension of the language of first-order predicate logic that allows to express statements about both statistical and subjective probabilities. Semantics for this representation language are developed that give rise to two distinct entailment relations: a relation ⊨ that models strict, probabilistically valid, inferences, and a relation that models inductive probabilistic inferences. The inductive entailment relation is obtained by implementing cross-entropy minimization in a preferred model semantics. A main objective of our approach is to ensure that for both entailment relations complete proof systems exist. This is achieved by allowing probability distributions in our semantic models that use non-standard probability values. A number of results are presented that show that in several important aspects the resulting logic behaves just like a logic based on real-valued probabilities alone.     

A Probabilistic Approach to Conditional Reasoning Development

How likely is the glass to break, given that it is heated? The present study asks questions such as this with or without the premise if the glass is heated, it breaks. A reduced problem (question without premise) measures the statistical dependency (conditional probability) of an event to occur, given that another has occurred. Such statistical dependency represents knowledge-based reasoning (inferring from “glass heated” to “its breaking”) and is a component of the response to the complete problem (question with premise). The complete problems therefore measure not only knowledge-based reasoning in terms of statistical dependencies (inductive component) but assumption-based reasoning (deductive component). Two experiments revealed: a) Knowledge-based reasoning continues to develop and attains adult levels at 7th grade for the problems tested, and b) assumption-based reasoning (deductive component) is reliable only for secondary school students (7th graders).     

A General Framework for Probabilistic Measures of Coherence

Studia Logica - Coherence is a property of propositions hanging together or dovetailing with each other. About two decades ago, formal epistemologists started to engage in the project of...     

Supervenience and Causation: A Probabilistic Approach

It is often argued that if a mentalproperty supervenes on a physical property, then (1)the mental property M ``inherits' its causal efficacyfrom the physical property P and (2) the causalefficacy of M reduces to that of P. However, once weunderstand the supervenience thesis and the concept ofcausation probabilistically, it turns out that we caninfer the causal efficacy of M from that of P andvice versa if and only if a certain condition, whichI call the ``line-up' thesis, holds. I argue that thesupervenience thesis entails neither this conditionnor its denial. I also argue that even when theline-up thesis holds true, reductionism about thecausal efficacy of the mental property doesn'tfollow.     

A Confucian Interpretation of Creativity

This article explores a Confucian interpretation of creativity with reference to two classics—Analects and Mencius. A Confucian understanding of creativity centers on yi (appropriateness) and is motivated by shu (empathy) for the purpose of broadening dao (Way). Confucian creativity is manifested in two main ways: novelty through original interpretations of the objective world; and appropriateness through flexible responses to concrete circumstances synchronically and diachronically. Two major implications for research on creativity are highlighted. The first is that a Confucian approach to creativity extends the existing research on personal creativity by foregrounding the moral and interpersonal elements. Secondly, Confucian creativity synthesizes novelty and appropriateness, thereby challenging the essentialization of creativity and creative abilities of East Asians. A Confucian conception of creativity transcends a narrow focus on specific creative acts to a broader consideration of the agents, relationships, socio-cultural contexts and related moral issues.     

A Behavioral Interpretation of Aesthetics

The Psychological Record - A behavioral interpretation of aesthetics will doubtless require a series of successive approximations to reach a wholly satisfactory formulation. The present article is...     

A Class of Probabilistic Unfolding Models for Polytomous Responses

By revisiting the approaches used to present the Rasch model for polytomous response, this paper uses the principle of the rating formulation (Andrich, 1978) to construct a class of unfolding models for polytomous responses in terms of a set of latent dichotomous unfolding variables. By anchoring the dichotomous unfolding variables involved at the same location, this paper presents a formulation of a very general class of unfolding models for ordered polytomous responses, of which the unfolding models for ordered polytomous responses proposed hitherto are special cases. Within this class, the analytic and measurement properties of the probabilistic functions are well interpreted in terms of the latitudes of acceptance parameters of the dichotomous unfolding models. Based on the general form of this class of unfolding models, some new models are readily specified. Copyright 2001 Academic Press.     

Probabilistic argumentation

Argumentation in the sense of a process of logical reasoning is a very intuitive and general methodology of establishing conclusions from defeasible premises. The core of any argumentative process is the systematical elaboration, exhibition, and weighting of possible arguments and counter-arguments. This paper presents the formal theory of probabilistic argumentation, which is conceived to deal with uncertain premises for which respective probabilities are known. With respect to possible arguments and counter-arguments of a hypothesis, this leads to probabilistic weights in the first place, and finally to an overall probabilistic judgment of the uncertain proposition in question. The resulting probabilistic measure is called degree of support and possesses the desired properties of non-monotonicity and non-additivity. Reasoning according to the proposed formalism is an simple and natural generalization of the two classical forms of probabilistic and logical reasoning, in which the two traditional questions of the probability and the logical deducibility of a hypothesis are replaced by the more general question of the probability of a hypothesis being logically deducible from the available knowledge base. From this perspective, probabilistic argumentation also contributes to the emerging area of probabilistic logics.     

Probabilistic unfolding

A probabilistic unfolding model is presented which makes it possible to scale stimuli and subjects simultaneously, without assumptions concerning the distribution of subjects or of stimuli. The applicability of the model is demonstrated in areas of attitude measurement where the assumption of normality is inadequate.     

Probabilistic epigenesis

The notion that phenotypic traits, including behavior, can be predetermined has slowly given way in biology and psychology over the last two decades. This shift in thinking is due in large part to the growing evidence for the fundamental role of developmental processes in the generation of the stability and variations in phenotype that researchers in developmental and evolutionary sciences seek to understand. Here I review the tenets of a metatheoretical model of development called probabilistic epigenesis (PE) and explore its implications for furthering our understanding of developmental and evolutionary processes. The PE framework emphasizes the reciprocity of influences within and between levels of an organism's developmental manifold (genetic activity, neural activity, behavior, and the physical, social, and cultural influences of the external environment) and the ubiquity of gene-environment interaction in the realization of all phenotypes.     

自我与启蒙:儒家精神的现代转化

18世纪的欧洲哲人视孔子为启蒙运动的守护神,而20世纪的中国启蒙者则要打倒孔家店。孰是孰非?或者一般而言,儒家与启蒙的关系到底如何?按照康德的说法,启蒙是人类脱离自己所加之于自己的不成熟状态。根据福柯的观点,启蒙则是一种不断追求超越和逾越界限的态度,包括变为不同的自我。在启蒙理念演变的背后,其实是伦理自我转向了审美自我。不同于西方的自我图式,儒家自我带有焦点-区域的特性,且自强不息,可依情境而变。20世纪初,面对国家危机,儒家精神继承者舍身毁家而救国,以特定的启蒙方式谋求民族独立。进入21世纪,面对意义体系重塑的契机,儒家自我应继续启蒙,将一颗活泼泼的仁心,安顿于现代理念和文明秩序之中,实现儒家精神的再次转化。     

汉语本体符号新释

汉语“本体”由“本”与“体”两个符号组成,截然不同于印欧语系的 ontology。汉语“本体”与“体”“本”构成一个内在统一的过程。中华先哲的问学之旅,即是立“本”生“道”、“本体”与“体”“本”的和合相生之旅。汉语本体构成了汉语思维进行诗性超越的根基,它独特的创新意识表现为追“本”溯源、返“本”开新,在这个意义上汉语本体与方法论是统一的。自现代以来,ontology 式本体之理解遮蔽了汉语“本体”的“本”来内涵,汉语“本体”符号亟待摆脱ontology 的“殖民”,而返回母语故乡。     

A Process Interpretation of Daoist Thought

Despite the fact that the Dao De Jing道德經 is one of the mos frequently translated texts in history,most of these translations share certain unexamined and problematic assumptions which often make it seem as though the text is irrational,incoherent,and full of non sequiturs.Frequently,these assumptions involve the imposition of historically anachronous,linguistically unsound,and philosophically problematic categories and attitudes onto the text.One of the main causes of the problem is the persistent tendency on the part of most translators to read the first line of the text as referring to or implying the existence of some kind of "eternal Dao." These are what I term "ontological "readings,as opposed to the "process" reading I will be articulating here.     

A Viconian Interpretation of Psychological Counseling

Western culture moves through cycles in which faith, logic, and power succeed each other as the dominant structuring principles. Therefore, counseling evolved in this sequence.     

Probabilistic contingency theories of animal conditioning: A critical analysis

Seven contingency theories of classical and instrumental conditioning were defined in relation to the contingency matrix and to six separate probabilities which can be derived from this matrix. These theories were compared on the basis of formal similarities and differences, and were judged against three separate empirical variables which have been discussed in the contingency literature: the duration of the intertrial interval, partial reinforcement, and negative contingencies between the two events of conditioning. All previous theories had some difficulty predicting the effects of one or more of these variables upon animal conditioning. Also, some formulas make the unusual prediction that there will be less conditioning when there is more than one conditioning trial. The paper concluded with an extensive discussion of the problems that are created by conditioning events with temporal extension; events which are then categorized by a contingency matrix which has no temporal character. Some possible solutions to the problems were discussed.