292 research outputs found
A logic for reasoning about knowledge of unawareness
In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as âAnn knows that Bill is aware of something Ann is not aware ofâ â without using a stronger statement such as âAnn knows that Bill is aware of p and Ann is not aware of pâ, for some particular p. In Halpern and RĂȘgo (2006, 2009b) (revisited in Halpern and RĂȘgo (2009a, 2013)) Halpern and RĂȘgo introduced a logic in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. Our logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The logic is less expressive than Halpernâs and RĂȘgoâs logic. It is, however, expressive enough to express all of the motivating examples in Halpern and RĂȘgo (2006, 2009b). In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete
Modal Logics with Hard Diamond-free Fragments
We investigate the complexity of modal satisfiability for certain
combinations of modal logics. In particular we examine four examples of
multimodal logics with dependencies and demonstrate that even if we restrict
our inputs to diamond-free formulas (in negation normal form), these logics
still have a high complexity. This result illustrates that having D as one or
more of the combined logics, as well as the interdependencies among logics can
be important sources of complexity even in the absence of diamonds and even
when at the same time in our formulas we allow only one propositional variable.
We then further investigate and characterize the complexity of the
diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers'
comments. Accepted at LFCS 201
Awareness Logic: A Kripke-based Rendition of the Heifetz-Meier-Schipper Model
Heifetz, Meier and Schipper (HMS) present a lattice model of awareness. The
HMS model is syntax-free, which precludes the simple option to rely on formal
language to induce lattices, and represents uncertainty and unawareness with
one entangled construct, making it difficult to assess the properties of
either. Here, we present a model based on a lattice of Kripke models, induced
by atom subset inclusion, in which uncertainty and unawareness are separate. We
show the models to be equivalent by defining transformations between them which
preserve formula satisfaction, and obtain completeness through our and HMS'
results.Comment: 18 pages, 2 figures, proceedings of DaLi conference 202
RankPL: A Qualitative Probabilistic Programming Language
In this paper we introduce RankPL, a modeling language that can be thought of
as a qualitative variant of a probabilistic programming language with a
semantics based on Spohn's ranking theory. Broadly speaking, RankPL can be used
to represent and reason about processes that exhibit uncertainty expressible by
distinguishing "normal" from" surprising" events. RankPL allows (iterated)
revision of rankings over alternative program states and supports various types
of reasoning, including abduction and causal inference. We present the
language, its denotational semantics, and a number of practical examples. We
also discuss an implementation of RankPL that is available for download
Palgol: A High-Level DSL for Vertex-Centric Graph Processing with Remote Data Access
Pregel is a popular distributed computing model for dealing with large-scale
graphs. However, it can be tricky to implement graph algorithms correctly and
efficiently in Pregel's vertex-centric model, especially when the algorithm has
multiple computation stages, complicated data dependencies, or even
communication over dynamic internal data structures. Some domain-specific
languages (DSLs) have been proposed to provide more intuitive ways to implement
graph algorithms, but due to the lack of support for remote access --- reading
or writing attributes of other vertices through references --- they cannot
handle the above mentioned dynamic communication, causing a class of Pregel
algorithms with fast convergence impossible to implement.
To address this problem, we design and implement Palgol, a more declarative
and powerful DSL which supports remote access. In particular, programmers can
use a more declarative syntax called chain access to naturally specify dynamic
communication as if directly reading data on arbitrary remote vertices. By
analyzing the logic patterns of chain access, we provide a novel algorithm for
compiling Palgol programs to efficient Pregel code. We demonstrate the power of
Palgol by using it to implement several practical Pregel algorithms, and the
evaluation result shows that the efficiency of Palgol is comparable with that
of hand-written code.Comment: 12 pages, 10 figures, extended version of APLAS 2017 pape
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
Shared Information -- New Insights and Problems in Decomposing Information in Complex Systems
How can the information that a set of random variables
contains about another random variable be decomposed? To what extent do
different subgroups provide the same, i.e. shared or redundant, information,
carry unique information or interact for the emergence of synergistic
information?
Recently Williams and Beer proposed such a decomposition based on natural
properties for shared information. While these properties fix the structure of
the decomposition, they do not uniquely specify the values of the different
terms. Therefore, we investigate additional properties such as strong symmetry
and left monotonicity. We find that strong symmetry is incompatible with the
properties proposed by Williams and Beer. Although left monotonicity is a very
natural property for an information measure it is not fulfilled by any of the
proposed measures.
We also study a geometric framework for information decompositions and ask
whether it is possible to represent shared information by a family of posterior
distributions.
Finally, we draw connections to the notions of shared knowledge and common
knowledge in game theory. While many people believe that independent variables
cannot share information, we show that in game theory independent agents can
have shared knowledge, but not common knowledge. We conclude that intuition and
heuristic arguments do not suffice when arguing about information.Comment: 20 page
Prioritized Repairing and Consistent Query Answering in Relational Databases
A consistent query answer in an inconsistent database is an answer obtained
in every (minimal) repair. The repairs are obtained by resolving all conflicts
in all possible ways. Often, however, the user is able to provide a preference
on how conflicts should be resolved. We investigate here the framework of
preferred consistent query answers, in which user preferences are used to
narrow down the set of repairs to a set of preferred repairs. We axiomatize
desirable properties of preferred repairs. We present three different families
of preferred repairs and study their mutual relationships. Finally, we
investigate the complexity of preferred repairing and computing preferred
consistent query answers.Comment: Accepted to the special SUM'08 issue of AMA
Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables
We show that Branching-time temporal logics CTL and CTL*, as well as
Alternating-time temporal logics ATL and ATL*, are as semantically expressive
in the language with a single propositional variable as they are in the full
language, i.e., with an unlimited supply of propositional variables. It follows
that satisfiability for CTL, as well as for ATL, with a single variable is
EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a
single variable is 2EXPTIME-complete,--i.e., for these logics, the
satisfiability for formulas with only one variable is as hard as satisfiability
for arbitrary formulas.Comment: Prefinal version of the published pape
Towards Logical Specification of Statistical Machine Learning
We introduce a logical approach to formalizing statistical properties of
machine learning. Specifically, we propose a formal model for statistical
classification based on a Kripke model, and formalize various notions of
classification performance, robustness, and fairness of classifiers by using
epistemic logic. Then we show some relationships among properties of
classifiers and those between classification performance and robustness, which
suggests robustness-related properties that have not been formalized in the
literature as far as we know. To formalize fairness properties, we define a
notion of counterfactual knowledge and show techniques to formalize conditional
indistinguishability by using counterfactual epistemic operators. As far as we
know, this is the first work that uses logical formulas to express statistical
properties of machine learning, and that provides epistemic (resp.
counterfactually epistemic) views on robustness (resp. fairness) of
classifiers.Comment: SEFM'19 conference paper (full version with errors corrected
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