Argumentation-Based Semantics for Logic Programs with First-Order Formulae

2016 ◽  
pp. 43-60 ◽  
Author(s):  
Phan Minh Dung ◽  
Tran Cao Son ◽  
Phan Minh Thang
Keyword(s):  
Logic Programs ◽  
First Order

scholarly journals Learning Relational Representations with Auto-encoding Logic Programs

2019 ◽  
Author(s):  
Sebastijan Dumancic ◽  
Tias Guns ◽  
Wannes Meert ◽  
Hendrik Blockeel
Keyword(s):  
Deep Learning ◽  
Relational Learning ◽  
Order Logic ◽  
First Order Logic ◽  
Relational Data ◽  
Logic Programs ◽  
Learning Methods ◽  
First Order ◽  
Relational Structures ◽  
Representation Language

Deep learning methods capable of handling relational data have proliferated over the past years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these methods aim at re-representing symbolic relational data in Euclidean space. They offer better scalability, but can only approximate rich relational structures and are less flexible in terms of reasoning. This paper introduces a novel framework for relational representation learning that combines the best of both worlds. This framework, inspired by the auto-encoding principle, uses first-order logic as a data representation language, and the mapping between the the original and latent representation is done by means of logic programs instead of neural networks. We show how learning can be cast as a constraint optimisation problem for which existing solvers can be used. The use of logic as a representation language makes the proposed framework more accurate (as the representation is exact, rather than approximate), more flexible, and more interpretable than deep learning methods. We experimentally show that these latent representations are indeed beneficial in relational learning tasks.

scholarly journals Composing programs in a rewriting logic for declarative programming

2003 ◽  
Vol 3 (2) ◽  
pp. 189-221 ◽  
Author(s):  
J. M. MOLINA-BRAVO ◽  
E. PIMENTEL
Keyword(s):  
Logic Programming ◽  
Declarative Programming ◽  
Rewriting Logic ◽  
Logic Programs ◽  
Alternative Semantics ◽  
Program Module ◽  
First Order ◽  
Natural Notion ◽  
Functional Logic ◽  
Simple Notion

Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for nondeterministic functional-logic programs. In the context of this formalism, we introduce a simple notion of program module as an open program which can be extended together with several mechanisms to combine them. These mechanisms are based on a reduced set of operations. However, the high expressiveness of these operations enable us to model typical constructs for program modularization like hiding, export/import, genericity/instantiation, and inheritance in a simple way. We also deal with the semantic aspects of the proposal by introducing an immediate consequence operator, and studying several alternative semantics for a program module, based on this operator, in the line of logic programming: the operator itself, its least fixpoint (the least model of the module), the set of its pre-fixpoints (term models of the module), and some other variations in order to find a compositional and fully abstract semantics w.r.t. the set of operations and a natural notion of observability.

Protected completions of first-order general logic programs

1990 ◽  
Vol 6 (2) ◽  
pp. 147-172 ◽  
Author(s):  
James J. Lu ◽  
V. S. Subrahmanian
Keyword(s):  
Logic Programs ◽  
First Order ◽  
General Logic

scholarly journals Induction of First-Order Decision Lists: Results on Learning the Past Tense of English Verbs

1995 ◽  
Vol 3 ◽  
pp. 1-24 ◽  
Author(s):  
R. J. Mooney ◽  
M. E. Califf
Keyword(s):  
Background Knowledge ◽  
Past Tense ◽  
Logic Programs ◽  
Decision Lists ◽  
First Order ◽  
New Class ◽  
The Past

This paper presents a method for inducing logic programs from examples that learns a new class of concepts called first-order decision lists, defined as ordered lists of clauses each ending in a cut. The method, called FOIDL, is based on FOIL (Quinlan, 1990) but employs intensional background knowledge and avoids the need for explicit negative examples. It is particularly useful for problems that involve rules with specific exceptions, such as learning the past-tense of English verbs, a task widely studied in the context of the symbolic/connectionist debate. FOIDL is able to learn concise, accurate programs for this problem from significantly fewer examples than previous methods (both connectionist and symbolic).

scholarly journals First-Order Modular Logic Programs and their Conservative Extensions (Extended Abstract)

2017 ◽  
Author(s):  
Amelia Harrison ◽  
Yuliya Lierler
Keyword(s):  
Logic Programming ◽  
Short Version ◽  
Logic Programs ◽  
Conservative Extension ◽  
International Conference ◽  
First Order ◽  
Modular Logic ◽  
Traditional Programs ◽  
The Common ◽  
Conservative Extensions

This paper introduces first-order modular logic programs, which provide a way of viewing answer set programs as consisting of many independent, meaningful modules. We also present conservative extensions of such programs. This concept helps to identify strong relationships between modular programs as well as between traditional programs. For example, we illustrate how the notion of a conservative extension can be used to justify the common projection rewriting. This is a short version of a paper was presented at the 32nd International Conference on Logic Programming (Harrison and Lierler, 2016).

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