Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive. While their formalism is quite general, it is restricted to fluents whose values are drawn from discrete finite domains, as opposed to the continuous domains seen in many robotic applications. In this work, we show how this limitation in that approach can be lifted. By dealing seamlessly with both discrete distributions and continuous densities within a rich theory of action, we provide a very general logical specification of how belief should change after acting and sensing in complex noisy domains.
From the perspective of dynamical systems, closest in spirit to our work here are knowledge representation languages for reasoning about action and knowledge, which we refer to as action logics. The situation calculus @cite_57 @cite_10 , which has been the sole focus of this paper, is one such language. There are others, of course, such as the event calculus @cite_77 , dynamic logic @cite_28 @cite_67 , the fluent calculus @cite_18 , and formalisms based on the stable model semantics @cite_64 .
@cite_67 @cite_18 @cite_64 @cite_28 @cite_57 @cite_77 @cite_10
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We start from Reiter’s solution to the frame problem in terms of successor state axioms and Scherl and Levesque’s extension to knowledge, as formulated by Lakemeyer and Levesque in their logic ES.While it was believed up to now that quantification over actions is a characteristic feature of Reiter’s solution, we here show that for a reasonably large subset of Reiter’s basic action theories one can do without.We do so by recasting restricted basic action theories in a propositional modal logic, viz. dynamic epistemic logic with public announcements and public assignments. Abstract We represent properties of actions in a logic programming language that uses both classical negation and negation as failure. The method is applicable to temporal projection problems with incomplete information, as well as to reasoning about the past. It is proved to be sound relative to a semantics of action based on states and transition functions. In this paper I combine the dynamic epistemic logic of Gerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The result is a new probabilistic dynamic epistemic logic, a logic for reasoning about probability, information, and information change that takes higher order information into account. Probabilistic epistemic models are defined, and a way to build them for applications is given. Semantics and a proof system is presented and a number of examples are discussed, including the Monty Hall Dilemma. Formal Logic can be used to represent knowledge of many kinds for many purposes. It can be used to formalize programs, program specifications, databases, legislation, and natural language in general. For many such applications of logic a representation of time is necessary. Although there have been several attempts to formalize the notion of time in classical first-order logic, it is still widely believed that classical logic is not adequate for the representation of time and that some form of non-classical Temporal Logic is needed. In this paper, we shall outline a treatment of time, based on the notion of event, formalized in the Horn clause subset of classical logic augmented with negation as failure. The resulting formalization is executable as a logic program. We use the term ‘‘event calculus’’ to relate it to the well-known ‘‘situation calculus’’ (McCarthy and Hayes 1969). The main difference between the two is conceptual: the situation calculus deals with global states whereas the event calculus deals with local events and time periods. Like the event calculus, the situation calculus can be formalized by means of Horn clauses augmented with negation by failure (Kowalski 1979). The main intended applications investigated in this paper are the updating of databases and narrative understanding. In order to treat both cases uniformly we have taken the view that an update consists of the addition of new knowledge to a knowledge base. The effect of explicit deletion of information in conventional databases is obtained without deletion by adding new knowledge about the end of the period of time for which the information holds. Modeling and implementing dynamical systems is a central problem in artificial intelligence, robotics, software agents, simulation, decision and control theory, and many other disciplines. In recent years, a new approach to representing such systems, grounded in mathematical logic, has been developed within the AI knowledge-representation community. This book presents a comprehensive treatment of these ideas, basing its theoretical and implementation foundations on the situation calculus, a dialect of first-order logic. Within this framework, it develops many features of dynamical systems modeling, including time, processes, concurrency, exogenous events, reactivity, sensing and knowledge, probabilistic uncertainty, and decision theory. It also describes and implements a new family of high-level programming languages suitable for writing control programs for dynamical systems. Finally, it includes situation calculus specifications for a wide range of examples drawn from cognitive robotics, planning, simulation, databases, and decision theory, together with all the implementation code for these examples. This code is available on the book's Web site.