13,260 research outputs found
Complexity of the interpretability logic IL
We show that the decision problem for the basic system of interpretability
logic IL is PSPACE-complete. For this purpose we present an algorithm which
uses polynomial space with respect to the complexity of a given formula. The
existence of such algorithm, together with the previously known PSPACE hardness
of the closed fragment of IL, implies PSPACE-completeness.Comment: 7 page
On Cognitive Preferences and the Plausibility of Rule-based Models
It is conventional wisdom in machine learning and data mining that logical
models such as rule sets are more interpretable than other models, and that
among such rule-based models, simpler models are more interpretable than more
complex ones. In this position paper, we question this latter assumption by
focusing on one particular aspect of interpretability, namely the plausibility
of models. Roughly speaking, we equate the plausibility of a model with the
likeliness that a user accepts it as an explanation for a prediction. In
particular, we argue that, all other things being equal, longer explanations
may be more convincing than shorter ones, and that the predominant bias for
shorter models, which is typically necessary for learning powerful
discriminative models, may not be suitable when it comes to user acceptance of
the learned models. To that end, we first recapitulate evidence for and against
this postulate, and then report the results of an evaluation in a
crowd-sourcing study based on about 3.000 judgments. The results do not reveal
a strong preference for simple rules, whereas we can observe a weak preference
for longer rules in some domains. We then relate these results to well-known
cognitive biases such as the conjunction fallacy, the representative heuristic,
or the recogition heuristic, and investigate their relation to rule length and
plausibility.Comment: V4: Another rewrite of section on interpretability to clarify focus
on plausibility and relation to interpretability, comprehensibility, and
justifiabilit
Interpretable Categorization of Heterogeneous Time Series Data
Understanding heterogeneous multivariate time series data is important in
many applications ranging from smart homes to aviation. Learning models of
heterogeneous multivariate time series that are also human-interpretable is
challenging and not adequately addressed by the existing literature. We propose
grammar-based decision trees (GBDTs) and an algorithm for learning them. GBDTs
extend decision trees with a grammar framework. Logical expressions derived
from a context-free grammar are used for branching in place of simple
thresholds on attributes. The added expressivity enables support for a wide
range of data types while retaining the interpretability of decision trees. In
particular, when a grammar based on temporal logic is used, we show that GBDTs
can be used for the interpretable classi cation of high-dimensional and
heterogeneous time series data. Furthermore, we show how GBDTs can also be used
for categorization, which is a combination of clustering and generating
interpretable explanations for each cluster. We apply GBDTs to analyze the
classic Australian Sign Language dataset as well as data on near mid-air
collisions (NMACs). The NMAC data comes from aircraft simulations used in the
development of the next-generation Airborne Collision Avoidance System (ACAS
X).Comment: 9 pages, 5 figures, 2 tables, SIAM International Conference on Data
Mining (SDM) 201
Lewis meets Brouwer: constructive strict implication
C. I. Lewis invented modern modal logic as a theory of "strict implication".
Over the classical propositional calculus one can as well work with the unary
box connective. Intuitionistically, however, the strict implication has greater
expressive power than the box and allows to make distinctions invisible in the
ordinary syntax. In particular, the logic determined by the most popular
semantics of intuitionistic K becomes a proper extension of the minimal normal
logic of the binary connective. Even an extension of this minimal logic with
the "strength" axiom, classically near-trivial, preserves the distinction
between the binary and the unary setting. In fact, this distinction and the
strong constructive strict implication itself has been also discovered by the
functional programming community in their study of "arrows" as contrasted with
"idioms". Our particular focus is on arithmetical interpretations of the
intuitionistic strict implication in terms of preservativity in extensions of
Heyting's Arithmetic.Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years
later
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