Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When Do Introspection Axioms Matter for Multi-Agent Epistemic Reasoning?   The early literature on epistemic logic in philosophy focused on reasoning
about the knowledge or belief of a single agent, especially on controversies
about "introspection axioms" such as the 4 and 5 axioms. By contrast, the later
literature on epistemic logic in computer science and game theory has focused
on multi-agent epistemic reasoning, with the single-agent 4 and 5 axioms
largely taken for granted. In the relevant multi-agent scenarios, it is often
important to reason about what agent A believes about what agent B believes
about what agent A believes; but it is rarely important to reason just about
what agent A believes about what agent A believes. This raises the question of
the extent to which single-agent introspection axioms actually matter for
multi-agent epistemic reasoning. In this paper, we formalize and answer this
question. To formalize the question, we first define a set of multi-agent
formulas that we call agent-alternating formulas, including formulas like Box_a
Box_b Box_a p but not formulas like Box_a Box_a p. We then prove, for the case
of belief, that if one starts with multi-agent K or KD, then adding both the 4
and 5 axioms (or adding the B axiom) does not allow the derivation of any new
agent-alternating formulas -- in this sense, introspection axioms do not
matter. By contrast, we show that such conservativity results fail for
knowledge and multi-agent KT, though they hold with respect to a smaller class
of agent-nonrepeating formulas.

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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol