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## The grand challenges and myths of neural-symbolic computation

Venue: | Recurrent Neural Networks- Models, Capacities, and Applications, number 08041 in Dagstuhl Seminar Proceedings, Dagstuhl, Germany, 2008. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl |

Citations: | 2 - 0 self |

### Citations

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Citation Context ...tion. We assume familiarity with neural networks models and only summarise used concepts. A neural network can be seen as a massively parallel distributed processor that stores experiential knowledge =-=[18]-=-. A multilayer perceptron (MLP) is composed of several layers of simple processing units, the artificial neurons. Typically, neural-symbolic systems use some simple network model to compute and learn ... |

3694 |
Learning internal representations by error propagation
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Citation Context ...TLK [9] uses ensembles of Connectionist Inductive Learning and Logic Programming (CILP) neural networks [6,26]. CILP networks are single hidden layer networks that can be trained with backpropagation =-=[27]-=-. In CILP, a Translation Algorithm maps a temporal logic program P into a single hidden layer neural network N such that N computes the least fixed-point of P. Let us illustrate the approach by presen... |

3239 | D.: Model checking
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Citation Context ...im is to construct computational models and technologies, I would prefer to name the area as Neural-Symbolic Computation. 2 L.C. Lamb results have shown how to offer richer knowledge representation, reasoning, and learning by means of non-classical computation in neural-symbolic systems [9,10,11,12]. This is an important development, since non-classical logics and models have offered solid foundations for computer science, including contributions to the basis of model checking, system specification and verification, reasoning in multi-agent and distributed systems and knowledge representation [13,14,15]. In addition, the construction of effective computational cognitive models has recently been pointed out by Valiant as great challenge for computing and cognitive sciences [16]. Further, the UK Computing Research Committee (UKCRC) and the British Computer Society have organised since 2002 an ambitious research enterprise which identified challenges that may lead to long-term positive effects not only for computer science, but also for neural-symbolic computation research [17], as we shall see in the sequel. At least two of the grand challenges in computing research listed in [17] are particul... |

2068 | Finding structures in time
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Citation Context ...lities. This turns temporal logic into an expressive non-classical logical systems, which perhaps explains the success of this logic in computer science, artificial intelligence and cognitive science =-=[12,13,20,21,22,23]-=-. It is now common knowledge that modal logics have become one of the outstanding logical languages used in computer science from theoretical foundations [13,15] to state-of-the-art hardware [14] and ... |

1895 |
Causality: Models, Reasoning, and Inference
- Pearl
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Citation Context ...tics of neural models, including uncertainty, conditional reasoning (i.e. what kind of implication A → B between formulae A and B we have in neural networks. Is it classical, conditional [32], causal =-=[33]-=- or probabilistic implication [34]). What kind of negation do we have in neural networks? Intuitionistic as in [10,35], classical, or negation as10 L.C. Lamb failure? The forthcoming book [5] promise... |

1857 |
Reasoning about Knowledge
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Citation Context ...ions for computer science, including contributions to the basis of model checking, system specification and verification, reasoning in multi-agent and distributed systems and knowledge representation =-=[13,14,15]-=-. In addition, the construction of effective computational cognitive models has recently been pointed out by Valiant as great challenge for computing and cognitive sciences [16]. Further, the UK Compu... |

1645 |
The temporal logic of programs
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Citation Context ... have had so much success in computer science that Amir PnueliThe Grand Challenges of Neural-Symbolic Computation 11 was awarded the ACM Turing Award in 1996 for laying its computational foundations =-=[41]-=-, and Edmund Clarke, E. Allen Emerson and Joseph Sifakis - pioneers of its most prominent application (model checking) - have been awarded the ACM Turing Award in 2007. As non-classical reasoning rese... |

477 |
On the proper treatment of connectionism
- Smolensky
- 1988
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Citation Context ...-Symbolic Computation In 1988, McCarthy raised this issue on the note Epistemological challenges for connectionism [45], a published commentary on Smolensky’s On the proper treatment of connectionism =-=[46]-=-. Propositional fixation assumes that neural networks cannot go beyond propositional logic. Several researchers have now addressed this issue, and have indicated that this is not necessarily the case.... |

360 |
Reasoning About Uncertainty.
- Halpern
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Citation Context ...ncertainty, conditional reasoning (i.e. what kind of implication A → B between formulae A and B we have in neural networks. Is it classical, conditional [32], causal [33] or probabilistic implication =-=[34]-=-). What kind of negation do we have in neural networks? Intuitionistic as in [10,35], classical, or negation as10 L.C. Lamb failure? The forthcoming book [5] promises to shed some light on this, but ... |

272 |
Seven myths of formal methods’,
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Citation Context ...s have show that modal and temporal logics (which correspond to the two-variable fragment of first-order logic [47]) can be effectively represented in neural 1 I draw inspiration from a paper by Hall =-=[44]-=- about the seven myths of formal methods.12 L.C. Lamb networks [9,10,11,48,49,50]. Bader, Hitzler, Hölldobler, and Witzel have proved that neural networks can generate models of first-order logic pro... |

267 | Data types as lattices
- Scott
- 1976
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Citation Context ...ue and warned the programming languages community that the λ-calculus did not have a model at that time. He then developed such model and alongside Strachey founded the area of denotational semantics =-=[39,40]-=- 3.4 Challenge 4: Model Checking Cognitive Systems Model checking [14] has been probably the most successful non-classical logic-based technology of the last 30 years. It is founded on temporal logics... |

235 |
Hierarchical ordering of sequential processes
- Dijkstra
- 1971
(Show Context)
Citation Context ... the following example [12]. We have applied a neural-symbolic approach to a classical problem of synchronisation in distributed environments, namely, the Dining Philosophers Problem, originally from =-=[30]-=-: n philosophers sit at a table, spending their time thinking and eating. In the centre of the table there is a plate of noodles, and a philosopher needs two forks to eat it. The number of forks on th... |

190 |
Many-dimensional modal logics: Theory and applications.
- Gabbay, Kurucz, et al.
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Citation Context ...oral, epistemic, conditional, intuitionistic, doxastic or many-dimensional modal logics, including, for instance, combinations of time and knowledge, time and belief, or space and time, to name a few =-=[13,15,24]-=-. In order to represent rich non-classical, symbolic knowledge in connectionist models, such as modal and temporal knowledge (which have been shown adequate in modelling multi-agent cognition [22]), o... |

184 | Knowledge-based artificial neural networks
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Citation Context ... in its infancy, they have proved effective learning systems in real world applications. Such applications have included power systems fault diagnosis, computational biology and DNA sequence analysis =-=[6,58]-=-. They have also been successfully used as model allowing for integrated learning and computation of arguments, including circular arguments [59]. Moreover, neural-symbolic systems have allowed for fu... |

144 |
The Harmonic Mind. From Neural Computation to Optimality-Theoretic Grammar
- Smolensky, Legendre
- 2005
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Citation Context ...ive models. 1 Introduction The construction of computational cognitive models integrating the connectionist and symbolic paradigms of artificial intelligence is a standing research issue in the field =-=[1,2,3,4,5]-=-. These models may lead to more effective and richer cognitive computational models, and to a better understanding of the computational processes and techniques of artificial intelligence, with benefi... |

129 | Why is modal logic so robustly decidable
- Vardi
- 1997
(Show Context)
Citation Context ...is is not necessarily the case. Recently, Garcez, Lamb and Gabbay, in several publications have show that modal and temporal logics (which correspond to the two-variable fragment of first-order logic =-=[47]-=-) can be effectively represented in neural 1 I draw inspiration from a paper by Hall [44] about the seven myths of formal methods.12 L.C. Lamb networks [9,10,11,48,49,50]. Bader, Hitzler, Hölldobler,... |

104 |
Connectionist modelling in psychology: A localist manifesto.
- Page
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Citation Context ...ive models. 1 Introduction The construction of computational cognitive models integrating the connectionist and symbolic paradigms of artificial intelligence is a standing research issue in the field =-=[1,2,3,4,5]-=-. These models may lead to more effective and richer cognitive computational models, and to a better understanding of the computational processes and techniques of artificial intelligence, with benefi... |

86 | Complete axiomatizations for reasoning about knowledge and branching time
- Meyden, Wong
(Show Context)
Citation Context .... The Ki modality is known as the knowledge operator. Kiα means that agent i knows α, where α is some propositional formula. One of the typical axioms of temporal logics of knowledge is Ki ○ α → ○Kiα =-=[28]-=-, where ○ denotes the next time temporal operator. This means that what an agent i knows today (Ki) about tomorrow (○α), she still knows tomorrow (○Kiα). In other words, this axiom states that an agen... |

65 | Advances in SHRUTI: a neurally motivated model of relational knowledge representation and rapid inference using temporal synchrony.
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Citation Context ...th benefits to computer and cognitive sciences. Several efforts have been made in this direction. However, most of them deal with symbolic knowledge expressed as production rules or logic programming =-=[6,7,8]-=-. Recently, several research ⋆ Usually, this research area is referred to as neural-symbolic integration. However, I see integration as a methodology of neural-symbolic computation. If our aim is to c... |

64 | An overview of temporal and modal logic programming. In:
- Orgun, Ma
- 1994
(Show Context)
Citation Context ...tate (possible world or time point), but also the analysis of how knowledge changes through time. In order to reason over time and represent knowledge evolution, we combine Temporal Logic Programming =-=[29]-=- and the knowledge operator Ki into a Connectionist Temporal Logic of Knowledge (CTLK). The implementation of Ki is analogous to that of □; we treat Ki as a universal modality as done in [15]. Definit... |

62 | A.K.: Logic programs and connectionist networks.
- Hitzler, Holldobler, et al.
- 2004
(Show Context)
Citation Context ...generate models of first-order logic programs [51,52,53]. Several researchers have also shown that neural-symbolic systems can learn or compute relations and fragments of first-order logics, see e.g. =-=[54,55,56,57]-=-. These results provide evidence that the field is maturing in terms of foundational results. 4.2 Myth 2: Neural-Symbolic Systems do Not Work in Practice This myth has been challenged. Even though neu... |

58 | Verifying multi-agent programs by model checking. Autonomous Agents and Multi-Agent Systems
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Citation Context ... believe that model checking connectionist models may lead to the successful development of applied connectionist systems. Recently, model checking has been useful in multi-agent systems applications =-=[42]-=-. We conjecture that model checking connectionist systems may offer us principles to understand the how such models work, leading to a better understanding of the neural computation process and provid... |

44 | A neuroidal architecture for cognitive computation.
- Valiant
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Citation Context ...ive models. 1 Introduction The construction of computational cognitive models integrating the connectionist and symbolic paradigms of artificial intelligence is a standing research issue in the field =-=[1,2,3,4,5]-=-. These models may lead to more effective and richer cognitive computational models, and to a better understanding of the computational processes and techniques of artificial intelligence, with benefi... |

42 |
Neural-symbolic learning systems: foundations and applications.
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- 2012
(Show Context)
Citation Context ...e models. 1 Introduction The construction of computational cognitive models integrating the connectionist and symbolic paradigms of artificial intelligence is a standing research issue in the field [1,2,3,4,5]. These models may lead to more effective and richer cognitive computational models, and to a better understanding of the computational processes and techniques of artificial intelligence, with benefits to computer and cognitive sciences. Several efforts have been made in this direction. However, most of them deal with symbolic knowledge expressed as production rules or logic programming [6,7,8]. Recently, several research ? Usually, this research area is referred to as neural-symbolic integration. However, I see integration as a methodology of neural-symbolic computation. If our aim is to construct computational models and technologies, I would prefer to name the area as Neural-Symbolic Computation. 2 L.C. Lamb results have shown how to offer richer knowledge representation, reasoning, and learning by means of non-classical computation in neural-symbolic systems [9,10,11,12]. This is an important development, since non-classical logics and models have offered solid foundations for c... |

38 | Toward a new massively parallel computational model for logic programming. In:
- Holldobler, Kalinke
- 1994
(Show Context)
Citation Context ...th benefits to computer and cognitive sciences. Several efforts have been made in this direction. However, most of them deal with symbolic knowledge expressed as production rules or logic programming =-=[6,7,8]-=-. Recently, several research ⋆ Usually, this research area is referred to as neural-symbolic integration. However, I see integration as a methodology of neural-symbolic computation. If our aim is to c... |

28 | The Connectionist Inductive Learning and Logic Programming System.
- Garcez, S, et al.
- 1999
(Show Context)
Citation Context ...,11]. 2.1 Connectionist Temporal Logics of Knowledge Connectionist Temporal Logic of Knowledge CTLK [9] uses ensembles of Connectionist Inductive Learning and Logic Programming (CILP) neural networks =-=[6,26]-=-. CILP networks are single hidden layer networks that can be trained with backpropagation [27]. In CILP, a Translation Algorithm maps a temporal logic program P into a single hidden layer neural netwo... |

25 | Dimensions of neural-symbolic integration - a structured survey.
- Bader, Hitzler
- 2005
(Show Context)
Citation Context ...l-symbolic systems, we need to understand how far neural-symbolic systems go as knowledge representation systems. Related to this challenge is ontology learning and representation in the semantic web =-=[37]-=- or in domains where temporal and epistemic dimensions are of relevance, such as cognitive modelling [38]. 3.3 Challenge 3: To Provide a Semantic Foundation for Neural-Symbolic Computation. Although s... |

22 | Connectionist inference models.
- Browne, Sun
- 2001
(Show Context)
Citation Context ... and Gabbay, in several publications have show that modal and temporal logics (which correspond to the two-variable fragment of first-order logic [47]) can be effectively represented in neural 1 I draw inspiration from a paper by Hall [44] about the seven myths of formal methods. 12 L.C. Lamb networks [9,10,11,48,49,50]. Bader, Hitzler, Holldobler, and Witzel have proved that neural networks can generate models of first-order logic programs [51,52,53]. Several researchers have also shown that neural-symbolic systems can learn or compute relations and fragments of first-order logics, see e.g. [54,55,56,57]. These results provide evidence that the field is maturing in terms of foundational results. 4.2 Myth 2: Neural-Symbolic Systems do Not Work in Practice This myth has been challenged. Even though neural-symbolic systems are still in its infancy, they have proved effective learning systems in real world applications. Such applications have included power systems fault diagnosis, computational biology and DNA sequence analysis [6,58]. They have also been successfully used as model allowing for integrated learning and computation of arguments, including circular arguments [59]. Moreover, neural-... |

21 |
On the unusual effectiveness of logic in computer science. The Bulletin of Symbolic Logic
- Halpern, Harper, et al.
(Show Context)
Citation Context ...lities. This turns temporal logic into an expressive non-classical logical systems, which perhaps explains the success of this logic in computer science, artificial intelligence and cognitive science =-=[12,13,20,21,22,23]-=-. It is now common knowledge that modal logics have become one of the outstanding logical languages used in computer science from theoretical foundations [13,15] to state-of-the-art hardware [14] and ... |

20 | Connectionist model generation: A first-order approach.
- Bader, Hitzler, et al.
- 2008
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Citation Context ... the seven myths of formal methods.12 L.C. Lamb networks [9,10,11,48,49,50]. Bader, Hitzler, Hölldobler, and Witzel have proved that neural networks can generate models of first-order logic programs =-=[51,52,53]-=-. Several researchers have also shown that neural-symbolic systems can learn or compute relations and fragments of first-order logics, see e.g. [54,55,56,57]. These results provide evidence that the f... |

14 |
Symbols among neurons. In:
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- 1985
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Citation Context |

13 |
Connectionist inference models. neural networks
- Browne, Sun
(Show Context)
Citation Context ...generate models of first-order logic programs [51,52,53]. Several researchers have also shown that neural-symbolic systems can learn or compute relations and fragments of first-order logics, see e.g. =-=[54,55,56,57]-=-. These results provide evidence that the field is maturing in terms of foundational results. 4.2 Myth 2: Neural-Symbolic Systems do Not Work in Practice This myth has been challenged. Even though neu... |

12 |
Denotational semantics.
- Tennent
- 1994
(Show Context)
Citation Context ...ue and warned the programming languages community that the λ-calculus did not have a model at that time. He then developed such model and alongside Strachey founded the area of denotational semantics =-=[39,40]-=- 3.4 Challenge 4: Model Checking Cognitive Systems Model checking [14] has been probably the most successful non-classical logic-based technology of the last 30 years. It is founded on temporal logics... |

12 | A connectionist inductive learning system for modal logic programming. In:
- Garcez, Lamb, et al.
- 2002
(Show Context)
Citation Context ...two-variable fragment of first-order logic [47]) can be effectively represented in neural 1 I draw inspiration from a paper by Hall [44] about the seven myths of formal methods.12 L.C. Lamb networks =-=[9,10,11,48,49,50]-=-. Bader, Hitzler, Hölldobler, and Witzel have proved that neural networks can generate models of first-order logic programs [51,52,53]. Several researchers have also shown that neural-symbolic systems... |

12 | A.: A fully connectionist model generator for covered first-order logic programs. In:
- Bader, Hitzler, et al.
- 2007
(Show Context)
Citation Context ... the seven myths of formal methods.12 L.C. Lamb networks [9,10,11,48,49,50]. Bader, Hitzler, Hölldobler, and Witzel have proved that neural networks can generate models of first-order logic programs =-=[51,52,53]-=-. Several researchers have also shown that neural-symbolic systems can learn or compute relations and fragments of first-order logics, see e.g. [54,55,56,57]. These results provide evidence that the f... |

11 |
Three problems in computer science.
- Valiant
- 2003
(Show Context)
Citation Context ...representation, reasoning, and learning by means of non-classical computation in neural-symbolic systems [9,10,11,12]. This is an important development, since non-classical logics and models have offered solid foundations for computer science, including contributions to the basis of model checking, system specification and verification, reasoning in multi-agent and distributed systems and knowledge representation [13,14,15]. In addition, the construction of effective computational cognitive models has recently been pointed out by Valiant as great challenge for computing and cognitive sciences [16]. Further, the UK Computing Research Committee (UKCRC) and the British Computer Society have organised since 2002 an ambitious research enterprise which identified challenges that may lead to long-term positive effects not only for computer science, but also for neural-symbolic computation research [17], as we shall see in the sequel. At least two of the grand challenges in computing research listed in [17] are particularly relevant to neural-symbolic computation research. It is expected over the next decades that studies on the architecture of brains and minds and journeys in nonclassical com... |

11 | L.C.: Reasoning about time and knowledge in neural-symbolic learning systems.
- Garcez, Lamb
- 2004
(Show Context)
Citation Context ...ted in a single model the two fundamental aspects of intelligent behaviour, namely reasoning and learning. We have applied the model in reasoning about distributed knowledge representation benchmarks =-=[9,25]-=-, intuitionistic reasoning [10], temporal synchronisation and learning [12]. Thus, the following logic definitions shall be useful, as we shall use temporal reasoning to analyse the effectiveness of n... |

10 |
Neural-Symbolic Cognitive Reasoning.
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Citation Context |

10 |
Elementary Logics: a Procedural Perspective.
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Citation Context ... distinction between classical and non-classical reasoning.4 L.C. Lamb In order to illustrate the difference between classical and non-classical logics let us consider temporal logic as described in =-=[19]-=-. Let us regard the assignment of truthvalues to the propositions as being a description of the world or situation with respect to a particular time t. In temporal logic, the value assigned to a propo... |

10 |
Epistemological challenges for connectionism.
- McCarthy
- 1988
(Show Context)
Citation Context ...these myths over the last decades. 1 4.1 Myth 1: The Propositional Fixation of Neural-Symbolic Computation In 1988, McCarthy raised this issue on the note Epistemological challenges for connectionism =-=[45]-=-, a published commentary on Smolensky’s On the proper treatment of connectionism [46]. Propositional fixation assumes that neural networks cannot go beyond propositional logic. Several researchers hav... |

10 | L.C.: Value-based argumentation frameworks as neural-symbolic learning systems.
- Garcez, Gabbay, et al.
- 2005
(Show Context)
Citation Context ...sis, computational biology and DNA sequence analysis [6,58]. They have also been successfully used as model allowing for integrated learning and computation of arguments, including circular arguments =-=[59]-=-. Moreover, neural-symbolic systems have allowed for full solutions of standard testbed for distributed knowledge representation and reasoning about uncertainty, time and knowledge. For instance, a fu... |

10 | On the unusual effectiveness of logic in computer science,
- Halpern, Harper, et al.
- 2001
(Show Context)
Citation Context ...out particular timepoints or intervals, and several interpretations of these states. Under a modal interpretation of time, one could refer to the truth-values of a proposition in a linear timeline (considering both past and future), a branching time interpretation with several futures using modalities such as always true in future/past, sometimes true in the future/past among several other possibilities. This turns temporal logic into an expressive non-classical logical systems, which perhaps explains the success of this logic in computer science, artificial intelligence and cognitive science [12,13,20,21,22,23]. It is now common knowledge that modal logics have become one of the outstanding logical languages used in computer science from theoretical foundations [13,15] to state-of-the-art hardware [14] and multi-agent technologies [22]. The toolbox of any AI researcher now includes modal logics, as they were found appropriate for researches in several areas of AI. Areas such as knowledge representation, planning and theorem proving also have been making extensive use of modal logics, be they temporal, epistemic, conditional, intuitionistic, doxastic or many-dimensional modal logics, including, for i... |

9 | A.: The core method: Connectionist model generation for first-order logic programs.
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Citation Context ... the seven myths of formal methods.12 L.C. Lamb networks [9,10,11,48,49,50]. Bader, Hitzler, Hölldobler, and Witzel have proved that neural networks can generate models of first-order logic programs =-=[51,52,53]-=-. Several researchers have also shown that neural-symbolic systems can learn or compute relations and fragments of first-order logics, see e.g. [54,55,56,57]. These results provide evidence that the f... |

9 |
The brain-machine disanalogy.
- Conrad
- 1989
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Citation Context ...ons. He reminds us that “Trying to cope or mimic life or lifelike behaviour in all scientific disciplines has generally produced disillusion after high initial hopes and hype.” Teuscher quotes Conrad =-=[62]-=-, one of the pioneers of bio-inspired computational models: “...no system can be at once highly structurally programmable, evolutionary efficient and computationally efficient” [62]. In order to justi... |

8 |
A.: Compiled Labelled Deductive Systems: A Uniform Presentation of Non-classical Logics.
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Citation Context ...ions for computer science, including contributions to the basis of model checking, system specification and verification, reasoning in multi-agent and distributed systems and knowledge representation =-=[13,14,15]-=-. In addition, the construction of effective computational cognitive models has recently been pointed out by Valiant as great challenge for computing and cognitive sciences [16]. Further, the UK Compu... |

7 |
Applying connectionist modal logics to distributed knowledge representation problems.
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- 2004
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Citation Context ...two-variable fragment of first-order logic [47]) can be effectively represented in neural 1 I draw inspiration from a paper by Hall [44] about the seven myths of formal methods.12 L.C. Lamb networks =-=[9,10,11,48,49,50]-=-. Bader, Hitzler, Hölldobler, and Witzel have proved that neural networks can generate models of first-order logic programs [51,52,53]. Several researchers have also shown that neural-symbolic systems... |

6 |
A.: Labelled natural deduction for conditional logics of normality.
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Citation Context ...l characteristics of neural models, including uncertainty, conditional reasoning (i.e. what kind of implication A → B between formulae A and B we have in neural networks. Is it classical, conditional =-=[32]-=-, causal [33] or probabilistic implication [34]). What kind of negation do we have in neural networks? Intuitionistic as in [10,35], classical, or negation as10 L.C. Lamb failure? The forthcoming boo... |

5 |
d’Avila Garcez: A Connectionist Cognitive Model for Temporal Synchronisation
- Lamb, Borges, et al.
- 2007
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Citation Context ... knowledge of seemingly incompatible areas, but which can benefit from each other. Recently, non-classical logics have been shown to be prone to integration with neural networks. The work reported in =-=[5,9,10,12,20]-=- has indicated that modal, temporal and (fragments of) non-classical logics knowledge can be successfully represented, computed and learned by connectionist models. [51,52,53] have show how to compute... |

5 |
Learning logic programs with neural networks.
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Citation Context ...generate models of first-order logic programs [51,52,53]. Several researchers have also shown that neural-symbolic systems can learn or compute relations and fragments of first-order logics, see e.g. =-=[54,55,56,57]-=-. These results provide evidence that the field is maturing in terms of foundational results. 4.2 Myth 2: Neural-Symbolic Systems do Not Work in Practice This myth has been challenged. Even though neu... |

4 |
L.C.: A connectionist computational model for epistemic and temporal reasoning.
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Citation Context ...stuhl.de/opus/volltexte/2008/14232 L.C. Lamb results have shown how to offer richer knowledge representation, reasoning, and learning by means of non-classical computation in neural-symbolic systems =-=[9,10,11,12]-=-. This is an important development, since non-classical logics and models have offered solid foundations for computer science, including contributions to the basis of model checking, system specificat... |

4 | Connectionist modal logic: Representing modalities in neural networks.
- Garcez, Lamb, et al.
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Citation Context ...stuhl.de/opus/volltexte/2008/14232 L.C. Lamb results have shown how to offer richer knowledge representation, reasoning, and learning by means of non-classical computation in neural-symbolic systems =-=[9,10,11,12]-=-. This is an important development, since non-classical logics and models have offered solid foundations for computer science, including contributions to the basis of model checking, system specificat... |

3 |
Connectionist computations of intuitionistic reasoning.
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Citation Context ...rmulae A and B we have in neural networks. Is it classical, conditional [32], causal [33] or probabilistic implication [34]). What kind of negation do we have in neural networks? Intuitionistic as in =-=[10,35]-=-, classical, or negation as10 L.C. Lamb failure? The forthcoming book [5] promises to shed some light on this, but research is still needed, as pointed out in [36]. This would be of great benefit to ... |

3 |
L.C.: Neural-symbolic systems and the case for non-classical reasoning.
- Garcez, Lamb
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Citation Context ...l networks? Intuitionistic as in [10,35], classical, or negation as10 L.C. Lamb failure? The forthcoming book [5] promises to shed some light on this, but research is still needed, as pointed out in =-=[36]-=-. This would be of great benefit to the community, as we would be able to understand the logical and computational limitations and expressiveness of logic-based connectionist systems. This is a hard c... |

3 | First-order deduction in neural networks. In:
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Citation Context |

3 |
Towards understanding the role of learning models in the dynamics of the minority game. In:
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Citation Context ... cognitive modelling [9,5]. It would be interesting, however, to analyse the reasoning and learning capabilities of neural-symbolic systems in economic multi-agent scenarios such as the minority game =-=[60,61]-=-. 4.3 Myth 3: Neural-Symbolic Systems are Not Biologically Plausible This myth is strongly related to the challenge 3.5 above. Some neural-symbolic systems draw inspiration from biological models. How... |

2 |
L.F.D.: Cognitive modelling of event ordering reasoning in imagistic domains. In:
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Citation Context ...systems. Related to this challenge is ontology learning and representation in the semantic web [37] or in domains where temporal and epistemic dimensions are of relevance, such as cognitive modelling =-=[38]-=-. 3.3 Challenge 3: To Provide a Semantic Foundation for Neural-Symbolic Computation. Although several sound translations have been done from fragments of logic programming to connectionist models, in ... |

2 |
Biologically uninspired computer science.
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- 2006
(Show Context)
Citation Context ... building effective computational models, that can be of benefit to humankind, be they biologically motivated, inspired or just mathematical abstractions with no relation to biological constructions. =-=[43]-=- offers an interesting analysis about the recent trends on biologically inspired computing, suggesting that one should look not only at biological models, but to unconventional (non-classical) and nov... |

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Distributed knowledge representation in neural-symbolic learning systems: A case study. In:
- Garcez, Lamb, et al.
- 2003
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Citation Context ...two-variable fragment of first-order logic [47]) can be effectively represented in neural 1 I draw inspiration from a paper by Hall [44] about the seven myths of formal methods.12 L.C. Lamb networks =-=[9,10,11,48,49,50]-=-. Bader, Hitzler, Hölldobler, and Witzel have proved that neural networks can generate models of first-order logic programs [51,52,53]. Several researchers have also shown that neural-symbolic systems... |

2 | L.C.: An information-theoretic analysis of memory bounds in a distributed resource allocation mechanism. In:
- Araujo, Lamb
- 2007
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Citation Context ... cognitive modelling [9,5]. It would be interesting, however, to analyse the reasoning and learning capabilities of neural-symbolic systems in economic multi-agent scenarios such as the minority game =-=[60,61]-=-. 4.3 Myth 3: Neural-Symbolic Systems are Not Biologically Plausible This myth is strongly related to the challenge 3.5 above. Some neural-symbolic systems draw inspiration from biological models. How... |

2 | A.: A connectionist cognitive model for temporal synchronisation and learning. In:
- Lamb, Borges, et al.
- 2007
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Citation Context ...s direction. However, most of them deal with symbolic knowledge expressed as production rules or logic programming [6,7,8]. Recently, several research ? Usually, this research area is referred to as neural-symbolic integration. However, I see integration as a methodology of neural-symbolic computation. If our aim is to construct computational models and technologies, I would prefer to name the area as Neural-Symbolic Computation. 2 L.C. Lamb results have shown how to offer richer knowledge representation, reasoning, and learning by means of non-classical computation in neural-symbolic systems [9,10,11,12]. This is an important development, since non-classical logics and models have offered solid foundations for computer science, including contributions to the basis of model checking, system specification and verification, reasoning in multi-agent and distributed systems and knowledge representation [13,14,15]. In addition, the construction of effective computational cognitive models has recently been pointed out by Valiant as great challenge for computing and cognitive sciences [16]. Further, the UK Computing Research Committee (UKCRC) and the British Computer Society have organised since 2002... |

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Reasoning and learning about past temporal knowledge in connectionist models. In:
- Borges, Lamb, et al.
- 2007
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Citation Context ...out particular timepoints or intervals, and several interpretations of these states. Under a modal interpretation of time, one could refer to the truth-values of a proposition in a linear timeline (considering both past and future), a branching time interpretation with several futures using modalities such as always true in future/past, sometimes true in the future/past among several other possibilities. This turns temporal logic into an expressive non-classical logical systems, which perhaps explains the success of this logic in computer science, artificial intelligence and cognitive science [12,13,20,21,22,23]. It is now common knowledge that modal logics have become one of the outstanding logical languages used in computer science from theoretical foundations [13,15] to state-of-the-art hardware [14] and multi-agent technologies [22]. The toolbox of any AI researcher now includes modal logics, as they were found appropriate for researches in several areas of AI. Areas such as knowledge representation, planning and theorem proving also have been making extensive use of modal logics, be they temporal, epistemic, conditional, intuitionistic, doxastic or many-dimensional modal logics, including, for i... |

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d’Avila Garcez, A.: Reasoning and learning about past temporal knowledge in connectionist models
- Borges, Lamb
- 2007
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Citation Context ...lities. This turns temporal logic into an expressive non-classical logical systems, which perhaps explains the success of this logic in computer science, artificial intelligence and cognitive science =-=[12,13,20,21,22,23]-=-. It is now common knowledge that modal logics have become one of the outstanding logical languages used in computer science from theoretical foundations [13,15] to state-of-the-art hardware [14] and ... |

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Axiomatic method.
- McCall
- 1995
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Citation Context ...icians axiomatise logical systems to present subject-matters as formal and coherent theories, allowing for the deduction of all propositions of a system from a well-defined set of initial assumptions =-=[31]-=-. Axiomatisations are used to understand proofs from initial assumptions, to allow the analysis of the complexity and structure of proofs. Computer scientists axiomatise logic-based theories to better... |

1 | A connectionist model for constructive modal reasoning. In:
- Garcez, Lamb, et al.
- 2005
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Citation Context ...rmulae A and B we have in neural networks. Is it classical, conditional [32], causal [33] or probabilistic implication [34]). What kind of negation do we have in neural networks? Intuitionistic as in =-=[10,35]-=-, classical, or negation as10 L.C. Lamb failure? The forthcoming book [5] promises to shed some light on this, but research is still needed, as pointed out in [36]. This would be of great benefit to ... |