8,660 research outputs found
Knowing Values and Public Inspection
We present a basic dynamic epistemic logic of "knowing the value". Analogous
to public announcement in standard DEL, we study "public inspection", a new
dynamic operator which updates the agents' knowledge about the values of
constants. We provide a sound and strongly complete axiomatization for the
single and multi-agent case, making use of the well-known Armstrong axioms for
dependencies in databases
Epistemic Logic with Partial Dependency Operator
In this paper, we introduce dependency modality
into epistemic logic so as to reason about
dependency relationship in Kripke models. The resulted dependence epistemic
logic possesses decent expressivity and beautiful properties. Several
interesting examples are provided, which highlight this logic's practical
usage. The logic's bisimulation is then discussed, and we give a sound and
strongly complete axiomatization for a sub-language of the logic
Bisimulation in Inquisitive Modal Logic
Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style
modal logic. In its epistemic incarnation, it extends standard epistemic logic
to capture not just the information that agents have, but also the questions
that they are interested in. Technically, InqML fits within the family of
logics based on team semantics. From a model-theoretic perspective, it takes us
a step in the direction of monadic second-order logic, as inquisitive modal
operators involve quantification over sets of worlds. We introduce and
investigate the natural notion of bisimulation equivalence in the setting of
InqML. We compare the expressiveness of InqML and first-order logic, and
characterise inquisitive modal logic as the bisimulation invariant fragments of
first-order logic over various classes of two-sorted relational structures.
These results crucially require non-classical methods in studying bisimulations
and first-order expressiveness over non-elementary classes.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Tool support for reasoning in display calculi
We present a tool for reasoning in and about propositional sequent calculi.
One aim is to support reasoning in calculi that contain a hundred rules or
more, so that even relatively small pen and paper derivations become tedious
and error prone. As an example, we implement the display calculus D.EAK of
dynamic epistemic logic. Second, we provide embeddings of the calculus in the
theorem prover Isabelle for formalising proofs about D.EAK. As a case study we
show that the solution of the muddy children puzzle is derivable for any number
of muddy children. Third, there is a set of meta-tools, that allows us to adapt
the tool for a wide variety of user defined calculi
Reducing Validity in Epistemic ATL to Validity in Epistemic CTL
We propose a validity preserving translation from a subset of epistemic
Alternating-time Temporal Logic (ATL) to epistemic Computation Tree Logic
(CTL). The considered subset of epistemic ATL is known to have the finite model
property and decidable model-checking. This entails the decidability of
validity but the implied algorithm is unfeasible. Reducing the validity problem
to that in a corresponding system of CTL makes the techniques for automated
deduction for that logic available for the handling of the apparently more
complex system of ATL.Comment: In Proceedings SR 2013, arXiv:1303.007
Extending Dynamic Doxastic Logic: Accommodating Iterated Beliefs And Ramsey Conditionals Within DDL
In this paper we distinguish between various kinds of doxastic theories. One distinction is between informal and formal doxastic theories. AGM-type theories of belief change are of the former kind, while Hintikka’s logic of knowledge and belief is of the latter. Then we distinguish between static theories that study the unchanging beliefs of a certain agent and dynamic theories that investigate not only the constraints that can reasonably be imposed on the doxastic states of a rational agent but also rationality constraints on the changes of doxastic state that may occur in such agents. An additional distinction is that between non-introspective theories and introspective ones. Non-introspective theories investigate agents that have opinions about the external world but no higher-order opinions about their own doxasticnstates. Standard AGM-type theories as well as the currently existing versions of Segerberg’s dynamic doxastic logic (DDL) are non-introspective. Hintikka-style doxastic logic is of course introspective but it is a static theory. Thus, the challenge remains to devise doxastic theories that are both dynamic and introspective. We outline the semantics for truly introspective dynamic doxastic logic, i.e., a dynamic doxastic logic that allows us to describe agents who have both the ability to form higher-order beliefs and to reflect upon and change their minds about their own (higher-order) beliefs. This extension of DDL demands that we give up the Preservation condition on revision. We make some suggestions as to how such a non-preservative revision operation can be constructed. We also consider extending DDL with conditionals satisfying the Ramsey test and show that Gärdenfors’ well-known impossibility result applies to such a framework. Also in this case, Preservation has to be given up
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