Tiago de Lima

‘KNOWABLE’ AS ‘KNOWN AFTER AN ANNOUNCEMENT’

Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ♦ϕ expresses that there is a truthful announcement ψ after which ϕ is true. This logic gives a perspective on Fitch’s knowability issues: for which formulas ϕ does it hold that ϕ → ♦Kϕ? We give various semantic results, and we show completeness for a Hilbert-style axiomatization of this logic. There is a natural generalization to a logic for arbitrary events.

Tableaux for Public Announcement Logic

Public announcement logic extends multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. In this article, we propose a labelled tableau calculus for this logic, and show that it decides satisfiability of formulas in deterministic polynomial space. Since this problem is known to be PSPACE-complete, it follows that our proof method is optimal.

From Situation Calculus to Dynamic Epistemic Logic

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.

A logic for reasoning about responsibility

One way to allocate tasks to agents is by ascribing them obligations. From obligations to be, agents are able to infer what are the forbidden, permitted and obligatory actions they may perform, by using the well-known Meyer’s reduction from obligations to be to obligations to do. However, we show through an example that this method is not completely adequate to guide agents’ decisions. We then propose a solution using, instead of obligations, the concept of ‘responsibility’. To formalise responsibility we use a multiagent extension of propositional dynamic logic as framework, and then we define some basic concepts, such as ‘agent ability’, also briefly discussing the problem of uniform strategies and a possible solution. In the last part, we show that our framework can be used in the specification of normative multiagent systems, by presenting an extensive running example.

A Tableau Method for Public Announcement Logics

Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose a labelled tableau-calculus for this logic. We also present an extension of the calculus for a logic of arbitrary announcements.

Epistemic actions and ontic actions: a unified logical framework

A tool includes a handle having a shank extended from one end for engaging with and for driving fasteners. A driving stem has an extension for engaging into the orifice of the shank and has an engaging hole for receiving and driving the fasteners. The shank and the driving stem are extended from one end of the handle such that the handle may apply a greater torque against the driving stem. A cover is pivotally coupled to the handle and has one or more wheel members for forming a roller skate shape. The shank has a clamping device for clamping the driving stem in place.

On the Dynamics of Institutional Agreements

In this work we continue the work initiated in [1], in which a logic of individual and collective acceptance was introduced. Our aim in this paper is to investigate the extension of the logic of acceptance by public announcements of formulas. The function of public announcements is to diminish the space of possible worlds accepted by agents and sets of agents while functioning as members of a given group, team, organization, institution, etc., x. If a set of agents C ends up with an empty set of worlds that they accept while functioning as members of x, then the agents in C do not identify themselves any longer with x. In such a situation the agents in C should have the possibility to join x again. To that aim we discuss at the end of the paper an operation which consists of an agent (or set of agents) joining a given group, team, organization, institution, etc.

Public announcements, public assignments and the complexity of their logic

We study the extension of public announcement logic PAL by public assignments, which we call PALA. Just as in the case of PAL, the standard procedure for deciding PALA validity, i.e. the use of so-called reduction axioms to translate PALA formulae into formulae in epistemic logic EL, may lead to exponential growth. In this paper, we show that such a price is not mandatory, for we provide a polynomial translation of PALA into EL. This is based on abbreviations of subformulae by new propositional letters. Such optimal translation also enables us to show the computational complexity of the problem of deciding PALA validity, which turns out to be coNP-complete in the single-agent case and PSPACE-complete in the multiagent case.

A Recursive Shortcut for CEGAR: Application To The Modal Logic K Satisfiability Problem

Counter-Example-Guided Abstraction Refinement (CEGAR) has been very successful in model checking. Since then, it has been applied to many different problems. It is especially proved to be a highly successful practical approach for solving the PSPACE complete QBF problem. In this paper, we propose a new CEGAR-like approach for tackling PSPACE complete problems that we call RECAR (Recursive Explore and Check Abstraction Refinement). We show that this generic approach is sound and complete. Then we propose a specific implementation of the RECAR approach to solve the modal logic K satisfiability problem. We implemented both CEGAR and RECAR approaches for the modal logic K satisfiability problem within the solver MoSaiC. We compared experimentally those approaches to the state-of-the-art solvers for that problem. The RECAR approach outperforms the CEGAR one for that problem and also compares favorably against the state-of-the-art on the benchmarks considered.

Tableaux for acceptance logic

We continue the work initiated in [1,2,3], where the acceptance logic, a modal logic for modelling individual and collective acceptances was introduced. This logic is aimed at capturing the concept of acceptance qua member of an institution as the kind of attitude that agents are committed to when they are “functioning as members of an institution”. Acceptance logic can also be used to model judgement aggregation: it deals with how a collective acceptance of the members of an institution about a certain fact φ is created from the individual acceptances of the members of the institution. The contribution of this paper is to present a tableau method for the logic of acceptance. The method automatically decides whether a formula of the logic of acceptance is satisfiable thereby providing an automated reasoning procedure for judgement aggregation in the logic of acceptance.