We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the given formula is true in that model. We discuss how to construct a model that represents an agent's knowledge in a number of different contexts, and then consider how to approach the model-checking problem.

data types are facilitated in Godel by its type and module systems. Thus, in order to describe the meta-programming facilities of Godel, a brief account of these systems is given. Each constant, function, predicate, and proposition in a Godel program must be specified by a language declaration. The type of a variable is not declared but inferred from its context within a particular program statement. To illustrate the type system, we give the language declarations that would be required for the program in Figure 1. BASE Name. CONSTANT Tom, Jerry : Name. PREDICATE Chase : Name * Name; Cat, Mouse : Name. Note that the declaration beginning BASE indicates that Name is a base type. In the statement Chase(x,y) !- Cat(x) & Mouse(y). the variables x and y are inferred to be of type Name. Polymorphic types can also be defined in Godel. They are constructed from the base types, type variables called parameters, and type constructors. Each constructor has an arity 1 attached to it. As an...

In this review of metaprogramming in logic we pay equal attention to theoretical and practical issues: the contents range from mathematical and logical preliminaries to implementation and applications in, e.g., software engineering and knowledge representation. The area is one in rapid development but we have emphasized such issues that are likely to be important for future metaprogramming languages and methodologies. 1 Introduction The term `metaprogramming' relates to `programming' as `metalanguage' relates to `language' and `metalogic' to `logic': programming where the data represent programs. It should be no surprise that metaprogramming with logic programming languages takes advantage of many results from metalogic. In the most general interpretation we would say that `metaprogramming ' refers to any kind of computer programming where the input or output represents programs. We will refer to a program of this kind as a metaprogram and to its data as object programs. Analogousl...

We present the basic principles and possible applications of systems capable of meta-reasoning and reflection. After a discussion of the seminal approaches, we outline our own perception of the state of the art, mainly but not only in computational logic and logic programming. We review relevat successful...

We are developing a multilevel metalogic programming language that we call Alloy. It is based on first-order predicate calculus extended with metalogical constructs. An Alloy program consists of a collection of theories, all in the same language, and a representation relation over these theories. The whole language is self-representable, including names for expressions with variables. A significant difference, as compared with many previous approaches, is that an arbitrary number of metalevels can be employed and that the object-meta relationship between theories need not be circular. The language is primarily intended for representation of knowledge and metaknowledge and is currently being used in research on hierarchical representation of legal knowledge. We believe that the language allows sophisticated expression and efficient automatic deduction of interesting sets of beliefs of agents. This paper aims to give a preliminary and largely informal definition of the core of the langua...

In the line of a syntactic treatment of modalities, many proposals have been presented consisting in an extension of a logic calculus with a meta-language for expressing facts about terms and sentences, and with an axiomatization of provability. These proposals differ in the use of the inference rules used to link the object level and meta-level theories; the formulation of these reflection rules is crucial since it affects the consistency of the extended calculus. We argue that reflection rules resulting in a conservative extension are too weak. On the other hand, well known results show that non conservative extensions often run into paradoxes. We propose a non conservative extension where useful theorems can be proved while consistency is retained. 1 INTRODUCTION The advantages of a syntactic approach to the representation of truth, knowledge and belief have been largely discussed in the literature [(McCarthy 1979), (Moore, 1977), (Konolige, 1982), (Perlis, 1985), ...