归纳推理和演绎推理的关系理论及其模型

推理是人类高级认知过程的一种,相关的心理学研究一般将其分为归纳推理和演绎推理两个方面。归纳推理是从特殊到一般的推理过程,与之相对的演绎推理则是从一般到特殊的过程。归纳推理和演绎推理的关系问题是当前心理推理研究领域的一个重点问题。这一问题主要有两种理论解释：一种是单过程理论,该理论认为归纳推理和演绎推理本质上是同一个认知过程,以单过程理论为基础构建的推理模型称为单维模型;另一种是双过程理论,认为归纳推理和演绎推理是两个不同的认知过程,并不同程度地受到启发和分析过程的影响。未来研究可多关注推理的时间进程,以及采用不同的研究方法对各自理论提供数据支持。     

Training propositional reasoning

Two experiments compared the effects of four training conditions on propositional reasoning. A syntactic training demonstrated formal derivations, in an abstract semantic training the standard truth-table definitions of logical connectives were explained, and a domain-specific semantic training provided thematic contexts for the premises of the reasoning task. In a control training, an inductive reasoning task was practised. In line with the account by mental models, both kinds of semantic training were significantly more effective than the control and the syntactic training, whereas there were no significant differences between the control and the syntactic training, nor between the two kinds of semantic training. Experiment 2 replicated this pattern of effects using a different set of syntactic and domain-specific training conditions.     

Formal Ontology and Mathematics. A Case Study on the Identity of Proofs

We propose a novel, ontological approach to studying mathematical propositions and proofs. By “ontological approach” we refer to the study of the categories of beings or concepts that, in their practice, mathematicians isolate as fruitful for the advancement of their scientific activity (like discovering and proving theorems, formulating conjectures, and providing explanations). We do so by developing what we call a “formal ontology” of proofs using semantic modeling tools (like RDF and OWL) developed by the computer science community. In this article, (i) we describe this new approach and, (ii) to provide an example, we apply it to the problem of the identity of proofs. We also describe open issues and further applications of this approach (for example, the study of purity of methods). We lay some foundations to investigate rigorously and at large scale intellectual moves and attitudes that underpin the advancement of mathematics through cognitive means (carving out investigationally valuable concepts and techniques) and social means (like communication, collaboration, revision, and criticism of specific categories, inferential patterns, and levels of analysis). Our approach complements other types of analysis of proofs such as reconstruction in a deductive system and examination through a proof-assistant.

     

Model theory of deduction: a unified computational approach

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.
Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we provide a formal foundation. We validate the theory through a computational model (UNICORE) which allows fine-grained predictions of subjects' performance in different reasoning domains.
The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.
Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure.     

Anatomy of deductive reasoning

Much of cognitive research on deductive reasoning has been preoccupied with advocating for or against visuospatial (mental model theory) or linguistic/syntactic (mental logic theory) models of logical reasoning. Neuroimaging studies bear on this issue by pointing to both language-based and visuospatial systems being engaged during logical reasoning, and by raising additional issues not anticipated by these cognitive theories. Here, the literature on the neural basis of deductive reasoning from the past decade is reviewed. Although these results might seem chaotic and inconsistent, we identify several interesting patterns and articulate their implications for cognitive theories of reasoning. Cognitive neuroscience data point away from a unitary system for logical reasoning and towards a fractionated system dynamically reconfigured in response to specific task and environmental cues.     

条件推理:“演绎”与“概率”两种实验研究范式之比较

本研究通过推理心理学研究中的“演绎”和“概率”两种实验范式设计对同一个班级的大学生参与者(实验一中N=57,实验二中N=43)进行先后两次有关条件推理的实验研究后,得出如下主要结果:(1)推理者在对不同的“纯形式条件命题本身的认可度”以及对由它们各自建构的同类型推理题的推理结果之间的作答反应模式之间的差异都很小且具有较高的一致性;(2)对由不同的“含具体内容的假言命题”本身的认可度之间以及由它们建构的同类型条件推理题的推理结果之间具有较大的差异性;(3)推理者对“演绎”和“概率”两种不同实验范式分别建构的内容近似的推进题进行推理时具有大致相同的作答反应趋势。由此可以推论推理者在“概率推理实验范式”中的作答或推理结果可以被视为只是对“演绎推理实验范式”的相应推理题给出“概率解”的心理加工过程。     

Formal reasoning in Japanese older adults: The role of metacognitive strategy,task content,and social factors

This study investigated the availability of deductive reasoning competence in late adulthood. Forty-six Japanese older (mean age =71 years) and 58 Japanese young adults (mean age =19.6 years) were assessed for formal or deductive reasoning using Overton's (1990) revision of the four-card selection task. For older adults, metacognitive strategy—operating as a procedure designed to access reasoning competence—resulted in enhanced performance levels. When the semantic content of the reasoning task involved emotional issues, however, the metacognitive strategy failed to facilitate reasoning performance. This suggests that reasoning competence is available in late adulthood but that performance is susceptible to contextual variables. Social factors were not significantly related to older adults' reasoning performance. Thus, assessment of these factors may have been based on too broad a definition to describe adequately the status of the older adults. For the young, only semantic task content was related to reasoning performance.     

The Formalization of Cultural Psychology. Reasons and Functions

In this paper I discuss two basic theses about the formalization of cultural psychology. First, I claim that formalization is a relevant, even necessary stage of development of this domain of science. This is so because formalization allows the scientific language to achieve a much needed autonomy from the commonsensical language of the phenomena that this science deals with. Second, I envisage the two main functions that formalization has to perform in the field of cultural psychology: on the one hand, it has to provide formal rules grounding and constraining the deductive construction of the general theory; on the other hand, it has to provide the devices for supporting the interpretation of local phenomena, in terms of the abductive reconstruction of the network of linkages among empirical occurrences comprising the local phenomena.     

Chinese Logic and the Absence of Theoretical Sciences in Ancient China

In this essay, I examine the nature of Chinese logic and Chinese sciences in the history of China. I conclude that Chinese logic is essentially analogical, and that the Chinese did not have theoretical sciences. I then connect these together and explain why the Chinese failed to develop theoretical sciences, even though they enjoyed an advanced civilization and great scientific and technological innovations. This is because a deductive system of logic is necessary for the development of theoretical sciences, and analogical logic cannot provide the deductive connections between a theory and empirical observations required by a theoretical science. This also offers a more satisfactory answer to the long-standing Needham Problem.     

Are there Reasons to Challenge a Symbolic Computationalist Approach in Explaining Deductive Reasoning?

The majority of the existing theories explaining deductive reasoning could be included in a classic computationalist approach of the cognitive processes. In fact, deductive reasoning could be seen to be the pinnacle of the symbolic computationalism, its last fortress to be defended in the face of new, dynamic, and ecological perspectives over cognition. But are there weak points in that position regarding deductive reasoning? What would be the reasons for which new perspectives could gain in credibility? What could be their most important tenets? The answers given to those questions in the paper include two main points. The first one is that the present empirical data could not sustain unambiguously one view over the other, that they are obtained in artificial experimental conditions, and that there are data that are not easily explainable using the traditional computationalist paradigm. The second one is that approaching the deductive reasoning from dynamic and ecological perspectives could have significant advantages. The most obvious one is the possibility to integrate more easily the research regarding the deductive reasoning with the results obtained in other domains of the psychology (especially in what respects the lower cognitive processes), in artificial intelligence or in neurophysiology. The reasons for that would be that such perspectives, as they are sketched in the paper, would imply, essentially, processes of second-order pattern formation and recognition (as it is the case for perception), embodied cognition, and dynamic processes as the brain ones are.     

Models and theories I: The semantic view revisited

The paper, as Part I of a two‐part series, argues for a hybrid formulation of the semantic view of scientific theories. For stage‐setting, it first reviews the elements of the model theory in mathematical logic (on whose foundation the semantic view rests), the syntactic and the semantic view, and the different notions of models used in the practice of science. The paper then argues for an integration of the notions into the semantic view, and thereby offers a hybrid semantic view, which at once secures the view's logical foundations and enhances its applicability. The dilemma of either losing touch with the practice of science or yielding up the benefits of the model theory is thus avoided.     

The Constitution as an Axiomatic System

The Constitution is considered as an informal axiomatic system. The strategy proposed by the authors rests on the following propositions: (1) axioms are considered as contextual definitions of those concepts by means of which they are formulated; and (2) the main requirement for this type of system is internal consistency. The first proposition is necessary for considering the Constitution as an informal axiomatic system, while the second is sufficient, because the approach proposed, apart from consistency, must certainly consider the requirements for formal axiomatic systems, such as independence and completeness. The authors argue that the Constitution can be compared to axiomatic constructions in modern science in the sense that is given in the research on the logic and methodology of deductive sciences. This analogy is appropriate to the extent to which constitutional provisions are interpreted as the basic elements of the legal system, just as in the formal sciences axioms are regarded as basic principles that define the main features of the formal system. This means that the Constitution itself is seen as coherent, consistent discourse that contextually defines the meaning of the basic terms of the legal system.     

Two types of empirical adequacy: a partial structures approach

The notion of empirical adequacy has received recent philosophical attention, especially within the framework of the semantic approach. Empirical adequacy, as explicated in the semantic approach, concerns the relationship between empirical substructures and some phenomena. The aim here is to differentiate this notion of empirical adequacy from one concerning the relationship between data and phenomena. Distinguishing each notion of empirical adequacy emphasizes different aspects of scientific practice—one concerning theory-development from the basis of an established theory, the other concerning theory-development from the basis of data-fitting, where established theory may not foster further development. To illustrate this contrast, an example from financial economics is considered.     

A theory of behavior interaction in dyads: A structuralist account

A theory from the behavioral and social sciences is presented from the structuralist point of view. A more comprehensive theory-net is outlined, some basic terms and core assumptions are formulated, and an expansion of the theory towards two intended applications is given. Finally, some results of a first empirical test of the theory are reported. The aim of the paper is to show that the structuralist account of scientific theories is not confined to mathematical theories from the natural sciences, but can also be applied to relatively informal constructions of the behavioral and social sciences.     

Human reasoning: Deduction rules or mental models, or both?

A good deal of energy is currently being expended into discovering the fundamental machinery underlying deductive reasoning. Is it based upon mental models (arrays) or deduction rules (propositions)? The appeal of finding a “grand unified theory” of reasoning is obvious, but the likelihood of achieving this must also be considered.

This paper discusses the use of experimental psychology in attempts to discover the processes associated with the fundamental reasoning mechanism. One particular problem is that individuals can use different strategies to solve reasoning problems. The consequences of this are assessed in relation to: (1) the assumptions underlying the experiments, (2) the choice of tasks and task presentations intended to enable the fundamental reasoning processes to be viewed directly, and (3) the power status of the theories and the nature of the evidence required to show that either theory is superior. Under close scrutiny the debate appears to be unresolvable by using empirical techniques. However, although the main conclusions are negative, it is suggested that approaches that directly investigate individual differences are likely to be useful alternatives.     

The Logic of Plausible Reasoning: A Core Theory

The paper presents a core theory of human plausible reasoning based on analysis of people's answers to everyday questions about the world. The theory consists of three parts:

• 1 a formal representation of plausible inference patterns; such as deductions, inductions, and analogies, that are frequently employed in answering everyday questions;
• 2 a set of parameters, such as conditional likelihood, typicality, and similarity, that affect the certainty of people's answers to such questions; and
• 3 a system relating the different plausible inference patterns and the different certainty parameters.

This is one of the first attempts to construct a formal theory that addresses both the semantic and parametric aspects of the kind of everyday reasoning that pervades. all of human discourse.     

A second-order relevance logic with modality

In this paper a system, RPF, of second-order relevance logic with S5 necessity is presented which contains a defined, notion of identity for propositions. A complete semantics is provided. It is shown that RPF allows for more than one necessary proposition. RPF contains primitive syntactic counterparts of the following semantic notions: (1) the reflexive, symmetrical, transitive binary alternativeness relation for S5 necessity, (2) the ternary Routley-Meyer alternativeness relation for implication, and (3) the Routley-Meyer notion of a prime intensional theory, as well as defined syntactic counterparts, of the semantic notions of a possible world and the Routley-Meyer ^* operator.     

Syntactic principles of heuristic-driven theory projection

Analogy making is a central construct in human cognition and plays an important role to explain cognitive abilities. While various psychologically or neurally inspired theories for analogical reasoning have been proposed, there is a lack of a logical foundation for analogical reasoning in artificial intelligence and cognitive science. We aim to close this gap and propose heuristic-driven theory projection (HDTP), a mathematically sound framework for analogy making. HDTP represents knowledge about the source and the target domain as first-order logic theories and compares them for structural commonalities using anti-unification. The paper provides an overview of the syntactic principles of HDTP, explains all phases of analogy making at a formal level, and illustrates these phases with examples.     

The Scandal of Deduction

This article provides the first comprehensive reconstruction and analysis of Hintikka’s attempt to obtain a measure of the information yield of deductive inferences. The reconstruction is detailed by necessity due to the originality of Hintikka’s contribution. The analysis will turn out to be destructive. It dismisses Hintikka’s distinction between surface information and depth information as being of any utility towards obtaining a measure of the information yield of deductive inferences. Hintikka is right to identify the failure of canonical information theory to give an account of the information yield of deductions as a scandal, however this article demonstrates that his attempt to provide such an account fails. It fails primarily because it applies to only a restricted set of deductions in the polyadic predicate calculus, and fails to apply at all to the deductions in the monadic predicate calculus and the propositional calculus. Some corollaries of these facts are a number of undesirable and counterintuitive results concerning the proposed relation of linguistic meaning (and hence synonymy) with surface information. Some of these results will be seen to contradict Hintikka’s stated aims, whilst others are seen to be false. The consequence is that the problem of obtaining a measure of the information yield of deductive inferences remains an open one. The failure of Hintikka’s proposal will suggest that a purely syntactic approach to the problem be abandoned in favour of an intrinsically semantic one.