315,189 research outputs found
The logic of epistemic justification
Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But these closure principles are only a small sample of the logical principles that we might consider. In this paper, I will outline four further logical principles that plausibly hold for justification and two which plausibly do not. While my primary aim is just to put these principles forward, I will use them to evaluate some different approaches to justification and (tentatively) conclude that a ‘normic’ theory of justification best captures its logic
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
Subset models for justification logic
We introduce a new semantics for justification logic based on subset
relations. Instead of using the established and more symbolic interpretation of
justifications, we model justifications as sets of possible worlds. We
introduce a new justification logic that is sound and complete with respect to
our semantics. Moreover, we present another variant of our semantics that
corresponds to traditional justification logic.
These types of models offer us a versatile tool to work with justifications,
e.g.~by extending them with a probability measure to capture uncertain
justifications. Following this strategy we will show that they subsume
Artemov's approach to aggregating probabilistic evidence
Complexity Jumps In Multiagent Justification Logic Under Interacting Justifications
The Logic of Proofs, LP, and its successor, Justification Logic, is a
refinement of the modal logic approach to epistemology in which
proofs/justifications are taken into account. In 2000 Kuznets showed that
satisfiability for LP is in the second level of the polynomial hierarchy, a
result which has been successfully repeated for all other one-agent
justification logics whose complexity is known.
We introduce a family of multi-agent justification logics with interactions
between the agents' justifications, by extending and generalizing the two-agent
versions of the Logic of Proofs introduced by Yavorskaya in 2008. Known
concepts and tools from the single-agent justification setting are adjusted for
this multiple agent case. We present tableau rules and some preliminary
complexity results. In several cases the satisfiability problem for these
logics remains in the second level of the polynomial hierarchy, while for
others it is PSPACE or EXP-hard. Furthermore, this problem becomes PSPACE-hard
even for certain two-agent logics, while there are EXP-hard logics of three
agents
- …