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Fibring Neural Networks
, 2004
"... Neuralsymbolic systems are hybrid systems that integrate symbolic logic and neural networks. The goal of neuralsymbolic integration is to benefit from the combination of features of the symbolic and connectionist paradigms of artificial intelligence. This paper introduces a new neural network ..."
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Neuralsymbolic systems are hybrid systems that integrate symbolic logic and neural networks. The goal of neuralsymbolic integration is to benefit from the combination of features of the symbolic and connectionist paradigms of artificial intelligence. This paper introduces a new neural network architecture based on the idea of fibring logical systems. Fibring allows one to combine di#erent logical systems in a principled way. Fibred neural networks may be composed not only of interconnected neurons but also of other networks, forming a recursive architecture. A fibring function then defines how this recursive architecture must behave by defining how the networks in the ensemble relate to each other, typically by allowing the activation of neurons in one network (A) to influence the change of weights in another network (B). Intuitively, this can be seen as training network B at the same time that one runs network A. We show that, in addition to being universal approximators like standard feedforward networks, fibred neural networks can approximate any polynomial function to any desired degree of accuracy, thus being more expressive than standard feedforward networks.
A quantum logic of down below
 Handbook of Quantum Logic, Quantum Structure, and Quantum Computation
"... The logic that was purposebuilt to accommodate the hopedfor reduction of arithmetic gave to language a dominant and pivotal place. Flowing from the founding efforts of Frege, Peirce, and Whitehead and Russell, this was a logic that incorporated proof theory into syntax, and in so doing made of gra ..."
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Cited by 15 (12 self)
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The logic that was purposebuilt to accommodate the hopedfor reduction of arithmetic gave to language a dominant and pivotal place. Flowing from the founding efforts of Frege, Peirce, and Whitehead and Russell, this was a logic that incorporated proof theory into syntax, and in so doing made of grammar
Valuebased argumentation frameworks as neuralsymbolic learning systems
 Journal of Logic and Computation
"... While neural networks have been successfully used in a number of machine learning applications, logical languages have been the standard for the representation of argumentative reasoning. In this paper, we establish a relationship between neural networks and argumentation networks, combining reasoni ..."
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Cited by 10 (3 self)
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While neural networks have been successfully used in a number of machine learning applications, logical languages have been the standard for the representation of argumentative reasoning. In this paper, we establish a relationship between neural networks and argumentation networks, combining reasoning and learning in the same argumentation framework. We do so by presenting a new neural argumentation algorithm, responsible for translating argumentation networks into standard neural networks. We then show a correspondence between the two networks. The algorithm works not only for acyclic argumentation networks, but also for circular networks, and it enables the accrual of arguments through learning as well as the parallel computation of arguments. Keywords: NeuralSymbolic Systems, Valuebased Argumentation Frameworks, Hybrid Systems. 1
Rulebased agents in temporalised defeasible logic
 NINTH PACIFIC RIM INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE. NUMBER 4099 IN LNAI
, 2006
"... This paper provides a framework based on temporal defeasible logic to reason about deliberative rulebased cognitive agents. Compared to previous works in this area our framework has the advantage that it can reason about temporal rules. We show that for rulebased cognitive agents deliberation is m ..."
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Cited by 9 (5 self)
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This paper provides a framework based on temporal defeasible logic to reason about deliberative rulebased cognitive agents. Compared to previous works in this area our framework has the advantage that it can reason about temporal rules. We show that for rulebased cognitive agents deliberation is more than just deriving conclusions in terms of their mental components. Our paper is an extension of [5,6] in the area of cognitive agent programming.
Connectionist Modal Logic: Representing Modalities in Neural Networks
"... Modal logics are amongst the most successful applied logical systems. Neural networks were proved to be effective learning systems. In this paper, we propose to combine the strengths of modal logics and neural networks by introducing Connectionist Modal Logics (CML). CML belongs to the domain of neu ..."
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Cited by 4 (2 self)
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Modal logics are amongst the most successful applied logical systems. Neural networks were proved to be effective learning systems. In this paper, we propose to combine the strengths of modal logics and neural networks by introducing Connectionist Modal Logics (CML). CML belongs to the domain of neuralsymbolic integration, which concerns the application of problemspecific symbolic knowledge within the neurocomputing paradigm. In CML, one may represent, reason or learn modal logics using a neural network. This is achieved by a Modalities Algorithm that translates modal logic programs into neural network ensembles. We show that the translation is sound, i.e. the network ensemble computes a fixedpoint meaning of the original modal program, acting as a distributed computational model for modal logic. We also show that the fixedpoint computation terminates whenever the modal program is wellbehaved. Finally, we validate CML as a computational model for integrated knowledge representation and learning by applying it to a wellknown testbed for distributed knowledge representation. This paves the way for a range of applications on integrated knowledge representation and learning, from practical reasoning to evolving multiagent systems.
The grand challenges and myths of neuralsymbolic computation
 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
"... Abstract. The construction of computational cognitive models integrating the connectionist and symbolic paradigms of artificial intelligence is a standing research issue in the field. The combination of logicbased inference and connectionist learning systems may lead to the construction of semanti ..."
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Abstract. The construction of computational cognitive models integrating the connectionist and symbolic paradigms of artificial intelligence is a standing research issue in the field. The combination of logicbased inference and connectionist learning systems may lead to the construction of semantically sound computational cognitive models in artificial intelligence, computer and cognitive sciences. Over the last decades, results regarding the computation and learning of classical reasoning within neural networks have been promising. Nonetheless, there still remains much do be done. Artificial intelligence, cognitive and computer science are strongly based on several nonclassical reasoning formalisms, methodologies and logics. In knowledge representation, distributed systems, hardware design, theorem proving, systems specification and verification classical and nonclassical logics have had a great impact on theory and realworld applications. Several challenges for neuralsymbolic computation are pointed out, in particular for classical and nonclassical computation in connectionist systems. We also analyse myths about neuralsymbolic computation and shed new light on them considering recent research advances.
A Connectionist Model for Constructive Modal Reasoning
"... We present a new connectionist model for constructive, intuitionistic modal reasoning. We use ensembles of neural networks to represent intuitionistic modal theories, and show that for each intuitionistic modal program there exists a corresponding neural network ensemble that computes the program. T ..."
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We present a new connectionist model for constructive, intuitionistic modal reasoning. We use ensembles of neural networks to represent intuitionistic modal theories, and show that for each intuitionistic modal program there exists a corresponding neural network ensemble that computes the program. This provides a massively parallel model for intuitionistic modal reasoning, and sets the scene for integrated reasoning, knowledge representation, and learning of intuitionistic theories in neural networks, since the networks in the ensemble can be trained by examples using standard neural learning algorithms. 1
On Gabbay’s fibring methodology for bayesian and neural networks
 In Laws and Models in Science, European Science Foundation (ESF). King’s College
"... This paper discusses how Gabbay’s fibring methodology originally aimed at combining logics can be applied also to combine subsymbolic structures such as Bayesian networks or neural networks. I start by commenting on the paper Recursive Causality in Bayesian Networks and SelfFibring Networks by J. ..."
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This paper discusses how Gabbay’s fibring methodology originally aimed at combining logics can be applied also to combine subsymbolic structures such as Bayesian networks or neural networks. I start by commenting on the paper Recursive Causality in Bayesian Networks and SelfFibring Networks by J. Williamson and D. Gabbay, which shows how Bayesian networks can be fibred. I then discuss how neural networks can be fibred in the same spirit, compare the Bayesian and neural approaches, and illustrate the fibring of Bayesian and neural networks by applying it to valuebased argumentation in legal reasoning. I conclude by offering a first account of how symbolic and subsymbolic systems such as logics and networks can be fibred together. 1
Towards a Connectionist Argumentation Framework
"... Abstract. While neural networks have been successfully used in a number of machine learning applications, logical languages have been the standard for the representation of legal and argumentative reasoning ..."
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Abstract. While neural networks have been successfully used in a number of machine learning applications, logical languages have been the standard for the representation of legal and argumentative reasoning
A Bayesian Computational Cognitive Model
"... Computational cognitive modeling has recently emerged as one of the hottest issues in the AI area. Both symbolic approaches and connectionist approaches present their merits and demerits. Although Bayesian method is suggested to incorporate advantages of the two kinds of approaches above, there is n ..."
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Computational cognitive modeling has recently emerged as one of the hottest issues in the AI area. Both symbolic approaches and connectionist approaches present their merits and demerits. Although Bayesian method is suggested to incorporate advantages of the two kinds of approaches above, there is no feasible Bayesian computational model concerning the entire cognitive process by now. In this paper, we propose a variation of traditional Bayesian network, namely Globally Connected and Locally Autonomic Bayesian Network (GCLABN), to formally describe a plausible cognitive model. The model adopts a unique knowledge representation strategy, which enables it to encode both symbolic concepts and their relationships within a graphical structure, and to generate cognition via a dynamic oscillating process rather than a straightforward reasoning process like traditional approaches. Then a simple simulation is employed to illustrate the properties and dynamic behaviors of the model. All these traits of the model are coincident with the recently discovered properties of the human cognitive process.