Explicit Evidence Systems with Common Knowledge

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

Gelechiidae Moths Are Capable of Chemically Dissolving the Pollen of Their Host Plants: First Documented Sporopollenin Breakdown by an Animal

Background: Many insects feed on pollen surface lipids and contents accessible through the germination pores. Pollen walls, however, are not broken down because they consist of sporopollenin and are highly resistant to physical and enzymatic damage. Here we report that certain Microlepidoptera chemically dissolve pollen grains with exudates from their mouthparts. Methodology/Principal Findings: Field observations and experiments in tropical China revealed that two species of Deltophora (Gelechioidea) are the exclusive pollinators of two species of Phyllanthus (Phyllanthaceae) on which their larvae develop and from which the adults take pollen and nectar. DNA sequences placed the moths and plants phylogenetically and confirmed that larvae were those of the pollinating moths; molecular clock dating suggests that the moth clade is younger than the plant clade. Captive moths with pollen on their mouthparts after 2-3 days of starvation no longer carried intact grains, and SEM photographs showed exine fragments on their proboscises. GC-MS revealed cis-b-ocimene as the dominant volatile in leaves and flowers, but GC-MS analyses of proboscis extracts failed to reveal an obvious sporopollenindissolving compound. A candidate is ethanolamine, which occurs in insect hemolymphs and is used to dissolve sporopollenin by palynologists. Conclusions/Significance: This is the first report of any insect and indeed any animal chemically dissolving pollen

Two ways to common knowledge

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.

Realizing public announcements by justifications

Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agent's belief. We present OPAL(K) and JPAL(K) , two alternative justification counterparts of Gerbrandy–Groeneveld's public announcement logic PAL(K) . We show that PAL(K) is the forgetful projection of both OPAL(K) and JPAL(K) . We also establish that JPAL(K) partially realizes PAL(K) . The question whether a similar result holds for OPAL(K) is still open