1,599 research outputs found
New results on rewrite-based satisfiability procedures
Program analysis and verification require decision procedures to reason on
theories of data structures. Many problems can be reduced to the satisfiability
of sets of ground literals in theory T. If a sound and complete inference
system for first-order logic is guaranteed to terminate on T-satisfiability
problems, any theorem-proving strategy with that system and a fair search plan
is a T-satisfiability procedure. We prove termination of a rewrite-based
first-order engine on the theories of records, integer offsets, integer offsets
modulo and lists. We give a modularity theorem stating sufficient conditions
for termination on a combinations of theories, given termination on each. The
above theories, as well as others, satisfy these conditions. We introduce
several sets of benchmarks on these theories and their combinations, including
both parametric synthetic benchmarks to test scalability, and real-world
problems to test performances on huge sets of literals. We compare the
rewrite-based theorem prover E with the validity checkers CVC and CVC Lite.
Contrary to the folklore that a general-purpose prover cannot compete with
reasoners with built-in theories, the experiments are overall favorable to the
theorem prover, showing that not only the rewriting approach is elegant and
conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page
Induction of Interpretable Possibilistic Logic Theories from Relational Data
The field of Statistical Relational Learning (SRL) is concerned with learning
probabilistic models from relational data. Learned SRL models are typically
represented using some kind of weighted logical formulas, which make them
considerably more interpretable than those obtained by e.g. neural networks. In
practice, however, these models are often still difficult to interpret
correctly, as they can contain many formulas that interact in non-trivial ways
and weights do not always have an intuitive meaning. To address this, we
propose a new SRL method which uses possibilistic logic to encode relational
models. Learned models are then essentially stratified classical theories,
which explicitly encode what can be derived with a given level of certainty.
Compared to Markov Logic Networks (MLNs), our method is faster and produces
considerably more interpretable models.Comment: Longer version of a paper appearing in IJCAI 201
Lazy Model Expansion: Interleaving Grounding with Search
Finding satisfying assignments for the variables involved in a set of
constraints can be cast as a (bounded) model generation problem: search for
(bounded) models of a theory in some logic. The state-of-the-art approach for
bounded model generation for rich knowledge representation languages, like ASP,
FO(.) and Zinc, is ground-and-solve: reduce the theory to a ground or
propositional one and apply a search algorithm to the resulting theory.
An important bottleneck is the blowup of the size of the theory caused by the
reduction phase. Lazily grounding the theory during search is a way to overcome
this bottleneck. We present a theoretical framework and an implementation in
the context of the FO(.) knowledge representation language. Instead of
grounding all parts of a theory, justifications are derived for some parts of
it. Given a partial assignment for the grounded part of the theory and valid
justifications for the formulas of the non-grounded part, the justifications
provide a recipe to construct a complete assignment that satisfies the
non-grounded part. When a justification for a particular formula becomes
invalid during search, a new one is derived; if that fails, the formula is
split in a part to be grounded and a part that can be justified.
The theoretical framework captures existing approaches for tackling the
grounding bottleneck such as lazy clause generation and grounding-on-the-fly,
and presents a generalization of the 2-watched literal scheme. We present an
algorithm for lazy model expansion and integrate it in a model generator for
FO(ID), a language extending first-order logic with inductive definitions. The
algorithm is implemented as part of the state-of-the-art FO(ID) Knowledge-Base
System IDP. Experimental results illustrate the power and generality of the
approach
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
SkILL - a Stochastic Inductive Logic Learner
Probabilistic Inductive Logic Programming (PILP) is a rel- atively unexplored
area of Statistical Relational Learning which extends classic Inductive Logic
Programming (ILP). This work introduces SkILL, a Stochastic Inductive Logic
Learner, which takes probabilistic annotated data and produces First Order
Logic theories. Data in several domains such as medicine and bioinformatics
have an inherent degree of uncer- tainty, that can be used to produce models
closer to reality. SkILL can not only use this type of probabilistic data to
extract non-trivial knowl- edge from databases, but it also addresses
efficiency issues by introducing a novel, efficient and effective search
strategy to guide the search in PILP environments. The capabilities of SkILL
are demonstrated in three dif- ferent datasets: (i) a synthetic toy example
used to validate the system, (ii) a probabilistic adaptation of a well-known
biological metabolism ap- plication, and (iii) a real world medical dataset in
the breast cancer domain. Results show that SkILL can perform as well as a
deterministic ILP learner, while also being able to incorporate probabilistic
knowledge that would otherwise not be considered
Inductive Logic Programming in Databases: from Datalog to DL+log
In this paper we address an issue that has been brought to the attention of
the database community with the advent of the Semantic Web, i.e. the issue of
how ontologies (and semantics conveyed by them) can help solving typical
database problems, through a better understanding of KR aspects related to
databases. In particular, we investigate this issue from the ILP perspective by
considering two database problems, (i) the definition of views and (ii) the
definition of constraints, for a database whose schema is represented also by
means of an ontology. Both can be reformulated as ILP problems and can benefit
from the expressive and deductive power of the KR framework DL+log. We
illustrate the application scenarios by means of examples. Keywords: Inductive
Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid
Knowledge Representation and Reasoning Systems. Note: To appear in Theory and
Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables
- …