The Complexity of Reasoning for Fragments of Autoepistemic Logic

Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning about his own beliefs. In this paper we analyze all Boolean fragments of autoepistemic logic with respect to the computational complexity of the three most common decision problems expansion existence, brave reasoning and cautious reasoning. As a second contribution we classify the computational complexity of counting the number of stable expansions of a given knowledge base. To the best of our knowledge this is the first paper analyzing the counting problem for autoepistemic logic

A logic for reasoning about knowledge of unawareness

In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of” – without using a stronger statement such as “Ann knows that Bill is aware of p and Ann is not aware of p”, for some particular p. In Halpern and Rêgo (2006, 2009b) (revisited in Halpern and Rêgo (2009a, 2013)) Halpern and Rêgo introduced a logic in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. Our logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The logic is less expressive than Halpern’s and Rêgo’s logic. It is, however, expressive enough to express all of the motivating examples in Halpern and Rêgo (2006, 2009b). In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete

A simple logic for reasoning about incomplete knowledge

International audienceThe semantics of modal logics for reasoning about belief or knowledge is often described in terms of accessibility relations, which is too expressive to account for mere epistemic states of an agent. This paper proposes a simple logic whose atoms express epistemic attitudes about formulae expressed in another basic propositional language, and that allows for conjunctions, disjunctions and negations of belief or knowledge statements. It allows an agent to reason about what is known about the beliefs held by another agent. This simple epistemic logic borrows its syntax and axioms from the modal logic KD. It uses only a fragment of the S5 language, which makes it a two-tiered propositional logic rather than as an extension thereof. Its semantics is given in terms of epistemic states understood as subsets of mutually exclusive propositional interpretations. Our approach offers a logical grounding to uncertainty theories like possibility theory and belief functions. In fact, we define the most basic logic for possibility theory as shown by a completeness proof that does not rely on accessibility relations

A Spatial-Epistemic Logic for Reasoning about Security Protocols

Reasoning about security properties involves reasoning about where the information of a system is located, and how it evolves over time. While most security analysis techniques need to cope with some notions of information locality and knowledge propagation, usually they do not provide a general language for expressing arbitrary properties involving local knowledge and knowledge transfer. Building on this observation, we introduce a framework for security protocol analysis based on dynamic spatial logic specifications. Our computational model is a variant of existing pi-calculi, while specifications are expressed in a dynamic spatial logic extended with an epistemic operator. We present the syntax and semantics of the model and logic, and discuss the expressiveness of the approach, showing it complete for passive attackers. We also prove that generic Dolev-Yao attackers may be mechanically determined for any deterministic finite protocol, and discuss how this result may be used to reason about security properties of open systems. We also present a model-checking algorithm for our logic, which has been implemented as an extension to the SLMC system.Comment: In Proceedings SecCo 2010, arXiv:1102.516

Hidden protocols: Modifying our expectations in an evolving world

When agents know a protocol, this leads them to have expectations about future observations. Agents can update their knowledge by matching their actual observations with the expected ones. They eliminate states where they do not match. In this paper, we study how agents perceive protocols that are not commonly known, and propose a semantics-driven logical framework to reason about knowledge in such scenarios. In particular, we introduce the notion of epistemic expectation models and a propositional dynamic logic-style epistemic logic for reasoning about knowledge via matching agentsÊ expectations to their observations. It is shown how epistemic expectation models can be obtained from epistemic protocols. Furthermore, a characterization is presented of the effective equivalence of epistemic protocols. We introduce a new logic that incorporates updates of protocols and that can model reasoning about knowledge and observations. Finally, the framework is extended to incorporate fact-changing actions, and a worked-out example is given. © 2013 Elsevier B.V

A Logic of Knowing How

In this paper, we propose a single-agent modal logic framework for reasoning about goal-direct "knowing how" based on ideas from linguistics, philosophy, modal logic and automated planning. We first define a modal language to express "I know how to guarantee phi given psi" with a semantics not based on standard epistemic models but labelled transition systems that represent the agent's knowledge of his own abilities. A sound and complete proof system is given to capture the valid reasoning patterns about "knowing how" where the most important axiom suggests its compositional nature.Comment: 14 pages, a 12-page version accepted by LORI