27 research outputs found
Ranking Revision Reloaded
In the context of a general revision framework, we propose and take a first look at revision strategies for epistemic ranking measures reaching beyond minimal Jeffrey-conditionalization, a variant of Spohn-style revision
A Method for Reasoning about other Agents\u27 Beliefs from Observations
Traditional work in belief revision deals with the question of what an agent should believe upon receiving new information. We will give an overview about what can be concluded about an agent based on an observation of its belief revision behaviour. The observation contains partial information about the revision inputs received by the agent and its beliefs upon receiving them. We will sketch a method for reasoning about past and future beliefs of the agent and predicting which inputs it accepts and rejects. The focus of this talk will be on different degrees of incompleteness of the observation and variants of the general question we are able to deal with
Algebraic Methods of Classifying Directed Graphical Models
Directed acyclic graphical models (DAGs) are often used to describe common
structural properties in a family of probability distributions. This paper
addresses the question of classifying DAGs up to an isomorphism. By considering
Gaussian densities, the question reduces to verifying equality of certain
algebraic varieties. A question of computing equations for these varieties has
been previously raised in the literature. Here it is shown that the most
natural method adds spurious components with singular principal minors, proving
a conjecture of Sullivant. This characterization is used to establish an
algebraic criterion for isomorphism, and to provide a randomized algorithm for
checking that criterion. Results are applied to produce a list of the
isomorphism classes of tree models on 4,5, and 6 nodes. Finally, some evidence
is provided to show that projectivized DAG varieties contain useful information
in the sense that their relative embedding is closely related to efficient
inference
Qualitative inequalities for squared partial correlations of a Gaussian random vector
We describe various sets of conditional independence relationships,
sufficient for qualitatively comparing non-vanishing squared partial
correlations of a Gaussian random vector. These sufficient conditions are
satisfied by several graphical Markov models. Rules for comparing degree of
association among the vertices of such Gaussian graphical models are also
developed. We apply these rules to compare conditional dependencies on Gaussian
trees. In particular for trees, we show that such dependence can be completely
characterized by the length of the paths joining the dependent vertices to each
other and to the vertices conditioned on. We also apply our results to
postulate rules for model selection for polytree models. Our rules apply to
mutual information of Gaussian random vectors as well.Comment: 21 pages, 13 figure
Algebra in probabilistic reasoning
This short expository paper outlines applications of computer algebra to the
implication problem of conditional independence for Gaussian random variables.
We touch on certificates for validity and invalidity of inference rules from
the perspective of reproducibility of research data, computational complexity
of the inference problem and draw a parallel to automated theorem proving in
synthetic geometry.Comment: 6 pages, 2 figures; minor update of the published articl
Reasoning consistently about inconsistency
Patching et al. and Hinde et al. in their work on
truth-space mass assignments, presented a semantic unification
function and a semantic separation function for mass assignment
logic that dealt with inconsistency. This paper takes these
two functions and while preserving the outside inconsistencies
shows how inconsistency can be reasoned about in a consistent
manner. This means that inconsistency that arises outside the
system need not enter the system, but needs to be represented
within the system, and can therefore be extracted appropriately
as output from the system to emerge as inconsistency on the
outside. The internal reasoning system need therefore only
concern itself with belief in truth, falsity and uncertainty
Proof theory for hybrid(ised) logics
Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. In a series of papers this process has been detailed and taken as a basis for a specification methodology for reconfigurable systems. The present paper extends this work by showing how a proof calculus (in both a Hilbert and a tableau based format) for the hybridised version of a logic can be systematically generated from a proof calculus for the latter. Such developments provide the basis for a complete proof theory for hybrid(ised) logics, and thus pave the way to the development of (dedicated) proof support.The authors are grateful to Torben Bräuner for helpful, inspiring discussions, and to the anonymous referees for their detailed comments.
This work is funded by ERDF—European Regional Development Fund, through the COMPETE Programme, and by National Funds through Fundação para a Ciência e a Tecnologia(FCT) within project PTDC/EEI-CTP/4836/2014. Moreover, the first and the second authors are sponsored by FCT grants SFRH/BD/52234/2013 and SFRH/BPD/103004/2014, respectively. M. Mar-tins is also supported by the EU FP7 Marie Curie PIRSES-GA-2012-318986 project GeTFun: Generalizing Truth-Functionality and FCT project UID/MAT/04106/2013 through CIDMA. L.Barbosa is further supported by FCT in the context of SFRH/B-SAB/113890/2015
Refinement in hybridised institutions
Hybrid logics, which add to the modal description of transition structures the ability to refer to specific
states, offer a generic framework to approach the specification and design of reconfigurable systems, i.e., systems
with reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response
to both external stimuli or internal performance measures. A formal representation of such systems is through
transition structures whose states correspond to the different configurations they may adopt. Therefore, each
node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics
of the services provided in the corresponding configuration. This paper characterises equivalence and refinement
for these sorts of models in a way which is independent of (or parametric on) whatever logic (propositional,
equational, fuzzy, etc) is found appropriate to describe the local configurations. A Hennessy–Milner like theorem
is proved for hybridised logics.This work is funded by ERDF-European Regional Development Fund, through the COMPETE Programme, and by National Funds through FCT within project FCOMP-01-0124-FEDER-028923 and by project NORTE-07-0124-FEDER-000060, co-financed by the North Portugal Regional Operational Programme (ON.2), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF). The work had also partial financial assistance by the project PEst-OE/MAT/UI4106/2014 at CIDMA, FCOMP-01-0124-FEDER-037281 at INESC TEC and the Marie Curie project FP7-PEOPLE-2012-IRSES (GetFun)