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In Praise of Belief Bases: Doing Epistemic Logic Without Possible Worlds

AAAI Conferences

We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and doxastic/epistemic alternative are primitive, in our semantics they are non-primitive but are defined from the concept of belief base. We provide a complete axiomatization and a decidability result for our logic.


Rethinking Epistemic Logic with Belief Bases

arXiv.org Artificial Intelligence

We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and doxastic/epistemic alternative are primitive, in our semantics they are non-primitive but are defined from the concept of belief base. We provide a complete axiomatization and prove decidability for our logic via a finite model argument. We also provide a polynomial embedding of our logic into Fagin & Halpern's logic of general awareness and establish a complexity result for our logic via the embedding.


Design of a Solver for Multi-Agent Epistemic Planning

arXiv.org Artificial Intelligence

The proliferation of agent-based and IoT technologies has e nabled the development of novel applications involving hundreds of agents. Considering that self-drivi ng cars and other autonomous devices that can control several aspects of our daily life are going to be avai lable en mass in just a few years it will not be long until massive systems of autonomous agents, each act ing upon its own knowledge and beliefs to achieve its own (or group) goals, become available and widel y deployed. To maximize the potentials of such autonomous systems, multi-agent planning and scheduling research [1, 8-10, 24, 28] will need to keep pace. Moreover crea ting a plan for multiple agents to achieve a goal will need to take into consideration agents' knowledge and beliefs, to account for aspects like trust, dishonesty, deception, and incomplete knowledge. The plan ning problem in this new setting is referred to as epistemic planning in the literature; that is epistemic planners are not only in terested in the state of the world but also in the knowledge or beliefs of the agents. Nevertheless, reasoning about knowledge and beliefs is not as direct as reasoning on the "physical" state of the world. That is because expressing, for example, belief relations between a group of agents often implies to consider nested and group beliefs that are not easily extracted from the state descrip tion by a human reader. For this reasons it is necessary to develop a complete and accessible action language to model multi-agent epistemic domains [2] and to advance al so in the study of epistemic solvers [4, 19, 23, 26, 34].


Parametric Constructive Kripke-Semantics for Standard Multi-Agent Belief and Knowledge (Knowledge As Unbiased Belief)

arXiv.org Artificial Intelligence

We propose parametric constructive Kripke-semantics for multi-agent KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions of two basic functional building blocks, namely bias (or viewpoint) and visibility, functioning also as the parameters of the doxastic and epistemic accessibility relation. The doxastic accessibility relates two possible worlds whenever the application of the composition of bias with visibility to the first world is equal to the application of visibility to the second world. The epistemic accessibility is the transitive closure of the union of our doxastic accessibility and its converse. Therefrom, accessibility relations for common and distributed belief and knowledge can be constructed in a standard way. As a result, we obtain a general definition of knowledge in terms of belief that enables us to view S5-knowledge as accurate (unbiased and thus true) KD45-belief, negation-complete belief and knowledge as exact KD45-belief and S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and accurate) KD45-belief, and all this generically for arbitrary functions of bias and visibility. Our results can be seen as a semantic complement to previous foundational results by Halpern et al. about the (un)definability and (non-)reducibility of knowledge in terms of and to belief, respectively.


Semantic results for ontic and epistemic change

arXiv.org Artificial Intelligence

We give some semantic results for an epistemic logic incorporating dynamic operators to describe information changing events. Such events include epistemic changes, where agents become more informed about the non-changing state of the world, and ontic changes, wherein the world changes. The events are executed in information states that are modeled as pointed Kripke models. Our contribution consists of three semantic results. (i) Given two information states, there is an event transforming one into the other. The linguistic correspondent to this is that every consistent formula can be made true in every information state by the execution of an event. (ii) A more technical result is that: every event corresponds to an event in which the postconditions formalizing ontic change are assignments to `true' and `false' only (instead of assignments to arbitrary formulas in the logical language). `Corresponds' means that execution of either event in a given information state results in bisimilar information states. (iii) The third, also technical, result is that every event corresponds to a sequence of events wherein all postconditions are assignments of a single atom only (instead of simultaneous assignments of more than one atom).