719 research outputs found
Angluin learning via logic
In this paper we will provide a fresh take on Dana Angluin's algorithm for learning using ideas from coalgebraic modal logic. Our work opens up possibilities for applications of tools & techniques from modal logic to automata learning and vice versa. As main technical result we obtain a generalisation of Angluin's original algorithm from DFAs to coalgebras for an arbitrary finitary set functor T in the following sense: given a (possibly infinite) pointed T-coalgebra that we assume to be regular (i.e. having an equivalent finite representation) we can learn its finite representation by asking (i) "logical queries" (corresponding to membership queries) and (ii) making conjectures to which the teacher has to reply with a counterexample. This covers (a known variant) of the original L* algorithm and the learning of Mealy/Moore machines. Other examples are bisimulation quotients of (probabilistic) transition systems
Extracting Rules from Neural Networks with Partial Interpretations
We investigate the problem of extracting rules, expressed in Horn logic, from
neural network models. Our work is based on the exact learning model, in which
a learner interacts with a teacher (the neural network model) via queries in
order to learn an abstract target concept, which in our case is a set of Horn
rules. We consider partial interpretations to formulate the queries. These can
be understood as a representation of the world where part of the knowledge
regarding the truthiness of propositions is unknown. We employ Angluin s
algorithm for learning Horn rules via queries and evaluate our strategy
empirically
Coalgebra Learning via Duality
Automata learning is a popular technique for inferring minimal automata
through membership and equivalence queries. In this paper, we generalise
learning to the theory of coalgebras. The approach relies on the use of logical
formulas as tests, based on a dual adjunction between states and logical
theories. This allows us to learn, e.g., labelled transition systems, using
Hennessy-Milner logic. Our main contribution is an abstract learning algorithm,
together with a proof of correctness and termination
Towards unsupervised ontology learning from data
Data-driven elicitation of ontologies from structured data is a well-recognized knowledge acquisition bottleneck. The development of efficient techniques for (semi-)automating this task is therefore practically vital - yet, hindered by the lack of robust theoretical foundations. In this paper, we study the problem of learning Description Logic TBoxes from interpretations, which naturally translates to the task of ontology learning from data.In the presented framework, the learner is provided with a set of positive interpretations (i.e., logical models) of the TBox adopted by the teacher. The goal is to correctly identify the TBox given this input. We characterize the key constraints on the models that warrant finite learnability of TBoxes expressed in selected fragments of the Description Logic ε λ and define corresponding learning algorithms.This work was funded in part by the National Research Foundation under Grant no. 85482
Learning definite Horn formulas from closure queries
A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be learnable under different query learning settings, such as learning from membership and equivalence queries or learning from entailment. We propose yet a different type of query: the closure query. Closure queries are a natural extension of membership queries and also a variant, appropriate in the context of definite Horn formulas, of the so-called correction queries. We present an algorithm that learns conjunctions of definite Horn clauses in polynomial time, using closure and equivalence queries, and show how it relates to the canonical Guigues–Duquenne basis for implicational systems. We also show how the different query models mentioned relate to each other by either showing full-fledged reductions by means of query simulation (where possible), or by showing their connections in the context of particular algorithms that use them for learning definite Horn formulas.Peer ReviewedPostprint (author's final draft
Exact Learning Description Logic Ontologies from Data Retrieval Examples
We investigate the complexity of learning description logic TBoxes in Angluin et al.’s framework of exact learning via queries posed to an oracle. We consider membership queries of the form “is individual a a certain answer to a data retrieval query q of ABox A and the target TBox?” and equivalence queries of the form “is a given TBox equivalent to the target TBox?”. We show that (i) DL-Lite TBoxes with role inclusions and ELI-concept expressions on the right-hand side of inclusions and (ii) EL TBoxes without complex concept expressions on the right-hand side of inclusions can be learned in polynomial time. Both results are proved by a non-trivial reduction to learning from subsumption examples. We also show that arbitrary EL TBoxes cannot be learned in polynomial time
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