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Nomenclatura Unesco > (11) Lógica > (1104) Lógica inductiva
- (1104.01) Inducción
- (1104.02) Intuicionismo
- (1104.03) Probabilidad
- (1104.99) Otras (especificar)
Nomenclatura Unesco > (11) Lógica > (1104) Lógica inductiva
Silva Bernardes, Juliana
International audience
Minato, Shin-ichi
Discrete structures are foundational material for computer science and mathematics, which are related to set theory, symbolic logic, inductive proof, graph theory, combinatorics, probability theory, etc. Many problems solved by computers can be decomposed into discrete structures using simple primitive algebraic operations. It is very important to represent discrete structures compactly and to execute efficiently tasks such as equivalency/validity checking, analysis of models, and optimization. Recently, BDDs (Binary Decision Diagrams) and ZDDs (Zero-suppressed BDDs) have attracted a great deal of attention, because they efficiently represent and manipulate large-scale combinational logic data, which are the basic discrete structures in various fields...
Rowe, RNS; Brotherston, J
© 2017 ACM.We describe a formal verification framework and tool implementation, based upon cyclic proofs, for certifying the safe termination of imperative pointer programs with recursive procedures. Our assertions are symbolic heaps in separation logic with user defined inductive predicates; we employ explicit approximations of these predicates as our termination measures. This enables us to extend cyclic proof to programs with procedures by relating these measures across the preand postconditions of procedure calls. We provide an implementation of our formal proof system in the CYCLIST theorem proving framework, and evaluate its performance on a range of examples drawn from the...
Dawar, Anuj; Lindell, Steven; Weinstein, Scott
The extensions of first-order logic with a least fixed point operators (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [AV91b] investigated the relation of these two logics in the absence of an ordering, using a mchine model of generic computation. In particular, they showed that the two languages have equivalent expressive power if and only if P = PSPACE. These languages can also be seen as fragments of an infinitary...
Morris, Gary
Kinship Analysis requires learning definitions of all kinship terms used in a target culture from data that is gathered incrementally through interviews with informants. We exploit a collection of previously learned kinship definitions from different cultures (logical “domain theories”) to minimize the cost of learning the definitions in a new domain theory. We use Transfer Learning and Inductive Logic Programming (ILP) to learn kinship definitions. We propose a novel method for identifying potential errors in the data by comparing our data with definitions in previously learned models of similar cultures. We actively ask informants to confirm or correct these potential...
Lin, Dianhuan; Dechter, Eyal; Ellis, Kevin M.; Tenenbaum, Joshua B.; Muggleton, Stephen H.
In recent years predicate invention has been underexplored as a bias reformulation mechanism within Inductive Logic Programming due to difficulties in formulating efficient search mechanisms. However, recent papers on a new approach called Meta-Interpretive Learning have demonstrated that both predicate invention and learning recursive predicates can be efficiently implemented for various fragments of definite clause logic using a form of abduction within a meta-interpreter. This paper explores the effect of bias reformulation produced by Meta-Interpretive Learning on a series of Program Induction tasks involving string transformations. These tasks have real-world applications in the use of spreadsheet technology. The existing implementation...
Dubba, KSR; Cohn, AG; Hogg, DC
Learning event models from videos has applications ranging from abnormal event detection to content based video retrieval. Relational learning techniques such as Inductive Logic Programming (ILP) hold promise for building such models, but have not been successfully applied to the very large datasets which result from video data. In this paper we present a novel supervised learning framework to learn event models from large video datasets (~2.5 million frames) using ILP. Efficiency is achieved via the learning from interpretations setting and using a typing system. This allows learning to take place in a reasonable time frame with reduced false positives....
Mbaye, Maissa; Krief, Francine; Soldano, Henry
Gaudel, Romaric; Sebag, Michèle; Cornuéjols, Antoine
This paper is concerned with Relational Support Vector Machines, at the intersection of Support Vector Machines (SVM) and Inductive Logic Programming or Relational Learning. The so-called phase transition framework, originally developed for constraint satisfaction problems, has been extended to relational learning and it has provided relevant insights into the limitations and difficulties thereof. The goal of this paper is to examine relational SVMs and specifically Multiple Instance (MI) Kernels along the phase transition framework. A relaxation of the MI-SVM problem formalized as a linear programming problem (LPP) is defined and we show that the LPP satisfiability rate induces a lower...
Cornuéjols, Antoine; Sebag, Michele
An ever greater range of applications call for learning from sequences. Grammar induction is one prominent tool for sequence learning, it is therefore important to know its properties and limits. This paper presents a new type of analysis for inductive learning. A few years ago, the discovery of a phase transition phenomenon in inductive logic programming proved that fundamental characteristics of the learning problems may affect the very possibility of learning under very general conditions. We show that, in the case of grammatical inference, while there is no phase transition when considering the whole hypothesis space, there is a much...
Enea, Constantin; Sighireanu, Mihaela; Wu, Zhilin
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas relating the inductive definitions. We propose a novel approach for generating these lemmas automatically which is based on simple syntactic criteria and deterministic strategies for applying them. Our approach focuses on iterative programs, although it can be applied to recursive programs as well, and specifications that describe not only the shape of the data structures, but also their content or their size. Empirically, we find that our approach is...
Brotherston, J; Fuhs, C; Pérez, JAN; Gorogiannis, N
We show that the satisfiability problem for the "symbolic heap" fragment of separation logic with general inductively defined predicates- which includes most fragments employed in program verification - is decidable. Our decision procedure is based on the computation of a certain fixed point from the definition of an inductive predicate, called its "base", that exactly characterises its satisfiability. A complexity analysis of our decision procedure shows that it runs, in the worst case, in exponential time. In fact, we show that the satisfiability problem for our inductive predicates is EXPTIME- complete, and becomes NP-complete when the maximum arity over all...
Antonopoulos, T; Gorogiannis, N; Haase, C; Kanovich, M; Ouaknine, J
We establish foundational results on the computational complexity of deciding entailment in Separation Logic with general inductive predicates whose underlying base language allows for pure formulas, pointers and existentially quantified variables. We show that entailment is in general undecidable, and ExpTime-hard in a fragment recently shown to be decidable by Iosif et al. Moreover, entailment in the base language is Π2P-complete, the upper bound even holds in the presence of list predicates. We additionally show that entailment in essentially any fragment of Separation Logic allowing for general inductive predicates is intractable even when strong syntactic restrictions are imposed. © 2014...
Antonopoulos, T; Gorogiannis, N; Haase, C; Kanovich, M; Ouaknine, J
We establish foundational results on the computational complexity of deciding entailment in Separation Logic with general inductive predicates whose underlying base language allows for pure formulas, pointers and existentially quantified variables. We show that entailment is in general undecidable, and ExpTime-hard in a fragment recently shown to be decidable by Iosif et al. Moreover, entailment in the base language is Π2P-complete, the upper bound even holds in the presence of list predicates. We additionally show that entailment in essentially any fragment of Separation Logic allowing for general inductive predicates is intractable even when strong syntactic restrictions are imposed. © 2014...
Brotherston, J; Gorogiannis, N; Petersen, RL
We describe the design and implementation of an automated theorem prover realising a fully general notion of cyclic proof. Our tool, called CYCLIST, is able to construct proofs obeying a very general cycle scheme in which leaves may be linked to any other matching node in the proof, and to verify the general, global infinitary condition on such proof objects ensuring their soundness. CYCLIST is based on a new, generic theory of cyclic proofs that can be instantiated to a wide variety of logics. We have developed three such concrete instantiations, based on: (a) first-order logic with inductive definitions; (b)...
Brotherston, J
We consider a cyclic approach to inductive reasoning in the setting of first-order logic with inductive definitions. We present a proof system for this language in which proofs are represented as finite, locally sound derivation trees with a "repeat function" identifying cyclic proof sections. Soundness is guaranteed by a well-foundedness condition formulated globally in terms of traces over the proof tree, following an idea due to Sprenger and Dam. However, in contrast to their work, our proof system does not require an extension of logical syntax by ordinal variables. A fundamental question in our setting is the strength of the...
Brotherston, J
We consider a cyclic approach to inductive reasoning in the setting of first-order logic with inductive definitions. We present a proof system for this language in which proofs are represented as finite, locally sound derivation trees with a "repeat function" identifying cyclic proof sections. Soundness is guaranteed by a well-foundedness condition formulated globally in terms of traces over the proof tree, following an idea due to Sprenger and Dam. However, in contrast to their work, our proof system does not require an extension of logical syntax by ordinal variables. A fundamental question in our setting is the strength of the...
Proceedings of ILP 2000, London, UK, July 24-27, 2000
Cussens, J
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic formulae themselves. We use Stochastic Logic Programs (SLPs) composed of labelled and unlabelled definite clauses to define the proof probabilities. We have a conservative extension of first-order reasoning, so that, far example, there is a one-one mapping between logical and random variables. We show how, in this framework, Inductive Logic Programming (ILP) can be used to induce the features of a loglinear model from data. We also compare...
Cussens, J