In this paper we introduce a new type of knowledge operator, called evidencebased knowledge, intended to capture the constructive core of common knowledge. An evidence-based knowledge system is obtained by augmenting a multi-agent logic of knowledge with a system of evidence assertions t:ϕ (“t is an evidence for ϕ”) based on the following plausible assumptions: 1) each axiom has evidence; 3) evidence is checkable; 3) any evidence implies individual knowledge for each agent. Normally, the following monotonicity property is also assumed: 4) any piece of evidence is compatible with any other evidence. We show that the evidence-based knowledge operator is a stronger version of the common knowledge operator. Evidence-based knowledge is free of logical omniscience, model-independent, and has a natural motivation. Furthermore, evidence-based knowledge can be presented by normal multi-modal logics, which are in the scope of well-developed machinery applicable to modal logic: epistemic models, normalized proofs, automated proof search, etc. 1

Starting off from the infinitary system for common knowledge over multi-modal epistemic logic presented in Alberucci and Jäger [1], we apply the finite model property to “finitize ” this deductive system. The result is a cut-free, sound and complete sequent calculus for common knowledge. 1

We first look at an existing infinitary sequent system for common knowledge for which there is no known syntactic cut-elimination procedure and also no known non-trivial bound on the proof-depth. We then present another infinitary sequent system based on nested sequents that are essentially trees and with inference rules that apply deeply inside of these trees. Thus we call this system “deep ” while we call the former system “shallow”. In contrast to the shallow system, the deep system allows to give a straightforward syntactic cut-elimination procedure. Since both systems can be embedded into each other, this also yields a syntactic cut-elimination procedure for the shallow system. For both systems we thus obtain an upper bound of ϕ20 onthe depth of proofs, where ϕ is the Veblen function. Key words: cut elimination, infinitary sequent system, nested sequents, common knowledge 1.

We give an optimal (exptime), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic. Our main contribution is a sound method to track unfulfilled eventualities “on the fly” which allows us to detect “bad loops” sooner rather than in multiple subsequent passes. We achieve this by propagating and updating the “status” of nodes throughout the underlying graph as soon as is possible. We give sufficient details to enable an easy implementation by others. Preliminary experimental results from our unoptimised OCaml implementation indicate that our algorithm is feasible.

ABSTRACT. Justification logics are epistemic logics that explicitly include justifications for the agents ’ knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting’s semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya’s minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic.

This paper presents a new model construction for a natural cut-free infinitary version K + ω (µ) of the propositional modal µ-calculus. Based on that the completeness of K + ω (µ) and the related system Kω(µ) can be established directly – no detour, for example through automata theory, is needed. As a side result we also obtain a finite, cut-free sound and complete system for the propositional modal µ-calculus. 1

It is not clear how a system for evidence based common knowledge should look like if common knowledge is treated as a greatest fixed point. The present paper is a preliminary step towards such a system. We argue that the standard induction rule is not well suited to axiomatize evidence based common knowledge. As an alternative, we study two different deductive systems for the logic of common knowledge. The first system makes use of an induction axiom whereas the second one is based on co-inductive proof theory. We show soundness and completeness for both systems. 1

et ses Applications ” organized the third instance of the Methods for Modalities Workshop (M4M-3) in Nancy, France. As in the previous instances of the workshop, the focus of the meeting was on reasoning methods, decision methods and proof tools for modal and modal-like languages and, also as in previous instances, the event was a great place to interchange ideas and obtain an up-to-date picture of the field.

We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor loops and passes extra information from children to parents to separate good loops from bad loops during backtracking. It is easy to implement, with potential for parallelisation, because it constructs a pseudo-model “on the fly ” by exploring each tableau branch independently. But its worst-case behaviour is 2EXPTIME rather than EXPTIME. A prototype implementation in the TWB

The notions of common knowledge or common belief play an important role in several areas of computer science (e.g. distributed systems, communication), in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of "agents", agreement or coordinated actions. In the following we will present several deductive systems for common knowledge above epistemic logics -- such as K, T, S4 and S5 -- with a fixed number of agents. We focus on structural and proof-theoretic properties of these calculi.