Introduction Many-valued logics in general and 3-valued logic in particular is an old subject which had its beginning in the work of Lukasiewicz [Luk]. Recently there is a revived interest in this topic, both for its own sake (see, e.g. [Ho]), and also because of its potential applications in several areas of computer science, like: proving correctness of programs ([Jo]), knowledge bases ([CP]) and Artificial Intelligence ([Tu]). There are, however, a huge number of 3-valued systems which logicians have studied throughout the years. The motivation behind them and their properties are not always clear and their proof theory is frequently not well developed. This state of affairs makes both the use of 3-valued logics and doing fruitful research on them rather difficult. Our first goal in this work is, accordingly, to identify and characterize a class of 3-valued logics which might be called natural. For this we use the general framework for characterizing and inve

In this paper, we present an analysis of planning with uncertain information regarding both the state of the world and the effects of actions using a Strips- or (propositional) Adl-style representation [4, 17]. We provide formal definitions of plans under incomplete information and conditional plans, and describe Plinth, a conditional linear planner based on these definitions. We also clarify the definition of the term "conditional action, " which has been variously used to denote actions with context-dependent effects and actions with uncertain outcomes. We show that the latter can, in theory, be viewed as a special case of the former but that to do so requires one to sacrifice the simple, singlemodel representation for one which can distinguish between a proposition and beliefs about that proposition. 1

The safety-critical nature of the application of knowledge-based systems to the field of medicine, demands the adoption of reliable engineering principles with a solid foundation for their construction. Logical languages with their inherent, precise notions of consistency, soundness and completeness offer such a foundation, thus promoting scrutinous engineering of medical knowledge. Moreover, logic techniques provide a powerful means for getting insight into the structure and meaning of medical knowledge used in medical problem solving. Unfortunately, logic is currently only used on a small scale for building practical medical knowledge-based systems. In this paper, the various approaches proposed in the literature are reviewed, and related to different types of knowledge and problem solving employed in the medical field. The appropriateness of logic for building medical knowledge-based expert systems is further motivated.

A clear understanding and formalization of actions is essential to computing, and especially so to reasoning about and constructing intelligent agents. Several approaches have been proposed over the years. However, most approaches concentrate on the causes and effects of actions, but do not give general characterizations of actions themselves. A useful formalization of actions would be based on a general, possibly nondiscrete, model of time that allows branching (to capture agents' choices). A desirable formalization would also allow actions to be of arbitrary duration and would permit multiple agents to act concurrently. We develop a branching-time framework that allows great flexibility in how time and action are modeled. We motivate and formalize several coherence constraints on our models, which capture some nice intuitions and validate some useful inferences relating actions with time. 1 Introduction Over the years, actions and time have garnered much research attent...

A review of the literature on evaluating reasoning systems reveals that it is a very broad area with wide variation in depth and breadth of research on metrics and tests. Consolidation is hampered by nonstandard terminology, differing methodologies, scattered application domains, unpublished algorithmic details, and the effects of domain content and context on the choice of metric and tests. The field of information metrology, which applies to reasoning as a kind of information processing, is still emerging from ad hoc experience in evaluating narrow kinds of information systems. This report begins to bring order to the area by categorizing reasoning systems according to their capabilities. The characteristics of each category can be used as a basis for evaluating and testing reasoning systems claiming to be in that category. Capabilities are analyzed along several dimensions, including representation languages, inference, and user and software interfaces. The report groups representation languages by their relation to first-order logic, and model-theoretic properties, such as soundness and completeness. Inference procedures are divided into deduction, induction, abduction, and analogical reasoning. Capabilities of user and software interfaces are described as they apply to

and queries’, Artificial Inteligence 53: 291–307.

: These notes survey modern logic's uses in formalizing subject matters, and its applications in artificial intelligence in particular. We assume familiarity with the elementary concepts of logic, and focus on logic's vocabulary for assessing, comparing, and iteratively improving tentative formulations of knowledge. We also consider logics of specific subjects, and present an annotated bibliography. Contents 1 Introduction 1 1.1 Elucidation of knowledge : : : : : : : : : : : : : : : : : : : : : 1 1.2 Analysis of representational systems : : : : : : : : : : : : : : : 1 1.3 Calculation of meaning : : : : : : : : : : : : : : : : : : : : : : 2 1.4 Logic and psychology : : : : : : : : : : : : : : : : : : : : : : : 2 2 The process of formalization 3 2.1 Formulation and formalization : : : : : : : : : : : : : : : : : : 3 2.2 Iterative formulation and formalization : : : : : : : : : : : : : 4 2.3 Formalization and mechanization : : : : : : : : : : : : : : : : 6 2.4 Formalization and intu...

Abstract. While the purpose of a conventional proof calculus is to axiomatise the set of valid sentences of a given logic, a refutation system, or complementary calculus, is concerned with axiomatising the invalid sentences. Instead of exhaustively searching for counter models for some sentence, refutation systems establish invalidity by deduction and thus in a purely syntactic way. Such systems are relevant not only for proof-theoretic reasons but also for realising deductive systems for nonmonotonic logics. In this paper, we introduce Gentzen-type refutation systems for two basic three-valued logics that allow to embed well-known three-valued logics relevant for AI and logic programming like that of Kleene, Łukasiewicz, Gödel, as well as three-valued paraconsistent logics. As an application of our calculus, we provide derived rules for Gödel’s three-valued logic, allowing to decide strong equivalence of logic programs under the answer-set semantics. 1