Non-Axiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the three simple systems, a Non-Axiomatic Logic is de ned. It has a term-oriented language and an experience-grounded semantics. It can uniformly represents and processes randomness, fuzziness, and ignorance. It can also uniformly carries out deduction, abduction, induction, and revision.

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An experience-grounded semantics is introduced for an intelligent reasoning system, which is adaptive, and works with insufficient knowledge and resources. According to this semantics, truth and meaning are defined with respect to the experience of the system — the truth value of a statement indicates the amount of available evidence, and the meaning of a term indicates its experienced relations with other terms. The major difference between experience-grounded semantics and modeltheoretic semantics is that the former does not assume the sufficiency of knowledge and resources. This approach provides new ideas to the solution of some important problems in cognitive science.

Properties of a few familiar structures (natural numbers, nested lists, lattices) are formally specified in Tarski-Givant's map calculus, with the aim of bringing to light new translation techniques that may bridge the gap between first-order predicate calculus and the map calculus. It is also highlighted to what extent a state-of-the-art theorem-prover for first-order logic, namely Otter, can be exploited not only to emulate, but also to reason about, map calculus. 3 1 Introduction Everybody remembers that Boole's Laws of thought (1854), Frege's Begriffsschrift (1879), and the Whitehead-Russell's Principia Mathematica (1910) have been three major milestones in the development of contemporary logic (cf. [3, 8, 15, 4]). Only a few people are aware that very important pre-Principia milestones were laid down by C.S. Peirce and E. Schroder and culminated in the monumental work [11, 12] on the Algebra der Logik . The "rather capricious line of historical development" of the algebraic for...

Abstract We are concerned with the problem of summarizing the contents of a coherent text. In this paper we argue that complex units of symbols like sentences, for example, are signs and the meaning of a text arises via their interaction. We introduce a model for the generation of summaries and illustrate its potential by a realistic example. Keywords: C.S. Peirce, logic, summarization, semiotics, meaning 1

Abstract. Peirce introduced an ingenious classification of signs and a theory of reasoning. Though he maintained that reasoning presupposes signs, to our best knowledge, he did not define a link between his two theories. In this paper we make a first attempt to reveal the possibility for such a relation, in the framework of a cognitively based model of sub-symbolic signs. 1

ViewGen, an algorithm and program for belief ascription, represents the beliefs of agents as explicit, partitioned proposition-sets known as environments. A way of extending View-Gen to the interpretation of metaphor, and in particular to the comprehension of metaphor within the belief spaces of particular agents, has been described elsewhere. The paper reports the further refinement and recent implementation of this approach, as well as summarizing the argument for the claim that ordinary non-metaphorical belief ascription and the transfer of information in metaphors can both be seen as different manifestations of a single environment-amalgamation process, one in which explicitly metaphorical amalgamations are triggered by "preference breaking " in the sentence being processed. This requires a consideration of the scoping of metaphor with respect to belief contexts, analogous to the scoping of quantification and definite descriptions with respect to such contexts. As a topic of ongoing and future work, the issue of mixed metaphor, of two distinct types, is briefly addressed. 1 ViewGen: The Basic Belief Engine A computational model of belief ascription is described in detail elsewhere [Wilks and Bien, 1979, 1983] [Ballim, 1987] [Wilks and Ballim, 1987] [Ballim and Wilks, in press] and is embodied in a prolog program called View-Gen. The basic algorithm of this model uses the notion of default reasoning to ascribe beliefs to other agents unless there is evidence to prevent the ascription. Perrault [1987, 1990] and Cohen and Levesque [1985] have also recently explored a belief and speech act logic based on a single explicit default axiom. As our previous work has shown for some years, the default ascription is basically correct, but the phenomena are more complex than are normally captured by an axiomatic approach. ViewGen also avoids certain counter-intuitive assumptions, such as the non-persistence of ignorance about any given proposition p [Perrault, 1990]. Also such systems

To integrate existing AI techniques into a consistent system, an intelligent core is needed, which is general and flexible, and can use the other techniques as tools to solve concrete problems. Such a system, NARS, is introduced. It is a general-purpose reasoning system developed to be adaptive and capable of working with insufficient knowledge and resources. Compared to traditional reasoning system, NARS is different in all major components (language, semantics, inference rules, memory structure, and control mechanism). Intelligence as a whole Artificial intelligence started as an attempt to build a general-purpose thinking machine with human-level intelligence. In the past decades, there were projects aimed at algorithms and architectures capturing the essence of intelligence, such as General Problem Solver (Newell and Simon,

First-order predicate logic meets many problems when used to explain or reproduce cognition and intelligence. These problems have a common nature, that is, they all exist outside mathematics, the domain for which mathematical logic was designed. Cognitive logic and mathematical logic are fundamentally different, and the former cannot be obtained by partially revising or extending the latter. A reasoning system using a cognitive logic is briefly introduced, which provides solutions to many problems in a unified manner. 1 Mathematical logic and cognition An automatic reasoning system usually consists of the following major components: 1. a formal language that represents knowledge, 2. a semantics that defines meaning and truth value in the language, 3. a set of inference rules that derives new knowledge, 4. a memory that stores knowledge, 5. a control mechanism that chooses premises and rules in each step. The first three components are usually referred to as a logic, or the logical part of the reasoning system, and the last two as an implementation of the logic, or the control part of the system. At the present time, the most influential theory for the logic part of reasoning systems is mathematical logic, especially, first-order predicate logic. For the control part, it is the theory of computability and computational complexity. Though these theories have been very successful in many domains, their application in cognitive science and artificial intelligence shows fundamental differences from human reasoning in similar situations.

Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topic-neutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought. Though these three notions of formality are by no means equivalent, they are frequently run together. The reason, I argue, is that modern talk of the formality of logic has its source in Kant, and these three notions come together in the context of Kant’s transcendental philosophy. Outside of this context (e.g., in Frege), they can come apart. Attending to this