The syntactic approach to epistemic logic avoids the logical omniscience problem by taking knowledge as primary rather than as defined in terms of possible worlds. In this study, we combine the syntactic approach with modal logic, using transition systems to model reasoning. We use two syntactic epistemic modalities: ‘knowing at least ’ a set of formulae and ‘knowing at most’ a set of formulae. We are particularly interested in models restricting the set of formulae known by an agent at a point in time to be finite. The resulting systems are investigated from the point of view of axiomatization and complexity. We show how these logics can be used to formalise non-omniscient agents who know some inference rules, and study their relationship to other systems of syntactic epistemic logics,

Abstract. An agent who bases his actions upon explicit logical formulae has at any given point in time a finite set of formulae he has computed. Closure or consistency conditions on this set cannot in general be assumed – reasoning takes time and real agents frequently have contradictory beliefs. This paper discusses a formal model of knowledge as explicitly computed sets of formulae. It is assumed that agents represent their knowledge syntactically, and that they can only know finitely many formulae at a given time. Existing syntactic characterizations of knowledge seem to be too general to have any interesting properties, but we extend the meta language to include an operator expressing that an agent knows at most a particular finite set of formulae. The specific problem we consider is the axiomatization of this logic. A sound system is presented. Strong completeness is impossible, so instead we characterize the theories for which we can get completeness. Proving that a theory actually fits this characterization, including proving weak completeness of the system, turns out to be non-trivial. One of the main results is a collection of algebraic conditions on sets of epistemic states described by a theory, which are sufficient for completeness. The paper is a contribution to a general abstract theory of resource bounded agents. Interesting results, e.g. complex algebraic conditions for completeness, are obtained from very simple assumptions, i.e. epistemic states as arbitrary finite sets and operators for knowing at least and at most. 1

Abstract. Standard syntactic assignments (SSAs) model knowledge directly rather than as truth in all possible worlds as in modal epistemic logic, by assigning arbitrary truth values to atomic epistemic formulae. It is a very general approach to epistemic logic, but has no interesting logical properties — partly because the standard logical language is too weak to express properties of such structures. In this paper we extend the logical language with a new operator used to represent the proposition that an agent “knows at most ” a given finite set of formulae and study the problem of strongly complete axiomatization of SSAs in this language. Since the logic is not semantically compact, a strongly complete finitary axiomatization is impossible. Instead we present, first, a strongly complete infinitary system, and, second, a strongly complete finitary system for a slightly weaker variant of the language. 1

Abstract. We introduce a logical language with nullary operators min(n), for each non-negative integer n, which mean ‘the reasoner has at least n different beliefs’. The resulting language allows us to express interesting properties of non-monotonic and resourcebounded reasoners. Other operators, such as ‘the reasoner has at most n different beliefs ’ and the operator introduced in [1, 4]: ‘the reasoner knows at most the formulae φ1,..., φn’, are definable using min(n). We introduce several syntactic epistemic logics with min(n) operators, and prove completeness and decidability results for those logics. 1

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Rule-based agents (for example, agents reasoning using ontology rules) are increasingly being employed in the implementation of web services and other situations in which the time taken to generate a response is critical. To be able to provide a response time guarantee for such systems, it is important to know how long the agent’s reasoning is going to take. In this paper, we describe an approach to establishing an upper bound on deliberation time of a system of rule-based agents. We propose a formal model of a system of rule-based agents which associates explicit costs with each rule application. This formal model can serve as an input to a model-checker, allowing upper bounds on deliberation time to be automatically verified. 1

Syntactic logics do not suffer from the problems of logical omniscience but are often thought to lack interesting properties relating to epistemic notions. By focusing on the case of rule-based agents, I develop a framework for modelling resource-bounded agents and show that the resulting models have a number of interesting properties.

Abstract. The core aim of this paper is to provide an overview of the benefits of a formal approach to information as being informative. It is argued that handling information-like objects can be seen as more fundamental than the notion of information itself. Starting from theories of semantic information, it is shown that these leave being informative out of the picture by choosing a logical framework which is essentially classical. Based on arguments in favour of logical pluralism, a formal approach of information handling inspired by non-classical logics is outlined. 1

michal,bezem¡ We discuss briefly the duality (or rather, complementarity) of system descriptions based on actions and transitions, on the one hand, and states and their changes, on the other. We settle for the latter and present a simple language, for describing state changes, which is parameterized by an arbitrary language for describing properties of the states. The language can be viewed as a simple fragment of step logic, admitting however various extensions by appropriate choices of the underlying logic. Alternatively, it can be seen as a very specific fragment of temporal logic (with a variant of ‘until ’ or ‘chop ’ operator), and is interpreted over dense (possibly continuous) linear time. The reasoning system presented here is sound, as well as strongly complete and decidable (provided that so is the parameter logic for reasoning about a single state). We give the main idea of the completeness proof and suggest a wide range of possible applications (action based descriptions, active logic, bounded agents), which is a simple consequence of the parametric character of both the language and the reasoning system. 1

In this position paper, we present a methodology for the formal evaluation of agent architectures. We argue that any agent architecture can be formally represented by a set of state transition systems. We then show how both qualitative and quantitative properties of an architecture can be evaluated using logical formulas interpreted in this set of state transition systems. In addition, we also provide a precise notion of what it means for an agent described in implementation specific terms to have or implement a given architecture.