A connectionist framework for reasoning: Reasoning with examples

… -symbolic integration: From …, 1997

An inference engine for a hybrid representation scheme based on neurules is presented. Neurules are a kind of hybrid rules that combine a symbolic (production rules) and a connectionist representation (adaline unit). The inference engine uses a connectionist technique, which is based on the 'firing potential', a measurement of the firing tendency of a neurule, and symbolic pattern matching. It is proved to be more efficient and natural than pure connectionist inference engines. Explanation of 'how' type can be provided in the form of if-then symbolic rules.

Artificial Intelligence, 1995

The paper presents a connectionist framework that is capable of representing and learning propositional knowledge. An extended version of propositional calculus is developed and is demonstrated to be useful for nonmonotonic reasoning, dealing with conflicting beliefs and for coping with inconsistency generated by unreliable knowledge sources. Formulas of the extended calculus are proved to be equivalent in a very strong sense to symmetric networks (like Hopfield networks and Boltzmann machines), and efficient algorithms are given for translating back and forth between the two forms of knowledge representation. A fast learning procedure is presented that allows symmetric networks to learn representations of unknown logic formulas by looking at examples. A connectionist inference engine is then sketched whose knowledge is either compiled from a symbolic representation or learned inductively from training examples. Experiments with large scale randomly generated formulas suggest that the parallel local search that is executed by the networks is extremely fast on average. Finally, it is shown that the extended logic can be used as a high-level specification language for connectionist networks, into which several recent symbolic systems may be mapped. The paper demonstrates how a rigorous bridge can be constructed that ties together the (sometimes opposing) connectionist and symbolic approaches.

Vietnam Journal of Computer Science, 2014

We present a simple, distributed reasoning system for the first order logic, which applies a connection calculus as an inference method. The calculus has been proposed by Bibel as a generalization of some other popular approaches, like the tableau calculus or the resolution-based inference. The system is constructed in a lean deduction style and it has been inspired to some extent by a sequential reasoner leanCoP, implemented in Prolog. Our reasoner has a form of a relational program in the Oz language. In this programming model, a computational strategy is a parameter of a program having a form of a special object called a search engine. Therefore, the same program can be run in various ways, particularly in parallel on distributed machines. For this purpose, we use a parallel search engine available on the Mozart platform, which is a programming environment for Oz. We also describe results of experiments for estimating a speedup obtained by the distributed processing.

Lecture Notes in Computer Science, 2012

For a long time, connectionist architectures have been criticized for having propositional fixation, lack of compositionality and, in general, for their weakness in representing sophisticated symbolic information and processing it. This work offers a novel approach that allows full integration of symbolic AI with the connectionist paradigm. We show how to encode and process relational knowledge using artificial neural networks (ANNs), such as Boltzmann Machines. The neural architecture uses a working memory (WM), consisting of pools of "binders", and a long-term synapticmemory that can store a large relational knowledge-base (KB). A compact variable binding mechanism is proposed which dynamically allocates ensembles of neurons when a query is clamped; retrieving KB items till a solution emerges in the WM. We illustrate the proposal through non-trivial predicate unification problems: knowledge items are only retrieved into the WM upon need, and unified, graphlike structures emerge at equilibrium as an activation pattern of the neural network. Our architecture is based on the fact that some attractor-based ANNs may be viewed as performing constraint satisfaction, where, at equilibrium, fixed-points maximally satisfy a set of weighted constraints. We show how to encode relational graphs as neural activation in WM and how to use constraints that are encoded in synapses, in order to retrieve and process such complex structures. Both procedural (the unification algorithm) and declarative knowledge (logic formulae) are first expressed as constraints and then used to generate (or learn) weighted synaptic connections. The architecture has no central control and is inherently robust to unit failures. Contrary to previous connectionist suggestions, this approach is expressive, compact, accurate, and goal directed. The mechanism is universal and has a simple underlying computational principle. As such, it may be further adapted for applications that combine the advantages of both connectionist and traditional symbolic AI and may be used in modeling aspects of human reasoning. BICA 2013 Symposium 16/6/2013 Dear BICA chairs, I'm happy to have the opportunity to submit our papers to the BICA 2013 conference Sincerely

Lecture Notes in Computer Science, 1996

Over the last years several new approaches for modeling situations, actions, and causality within a deductive framework were proposed. These new approaches treat the facts about a situation as resources, which are consumed and produced by actions. In this paper we extend one of these approaches, viz. an equational logic approach, by reifying actions to become resources as well. Using the concept of a membrane we show how abstractions and hierarchical planning can be modeled in such an equational logic. Moreover, we rigorously prove that the extended equational logic program can be mapped onto the so-called chemical abstract machine . As this machine is a model for parallel processes this may lead to a parallel computational model for reasoning about situations, actions, and causality.

Knowledge-Based Systems, 1995

The relationship between symbolism and connectionism has been one of the major issues in recent artificial intelligence research. An increasing number of researchers from each side have tried to adopt the desirable characteristics of the approach. A major open question in this field is the extent to which a connectionist architecture can accommodate basic concepts of symbolic inference, such as a dynamic variable binding mechanism and a rule and fact encoding mechanism involving nary predicates. One of the current leaders in this area is the connectionist rule-based system proposed by Shastri and Ajjanagadde. The paper demonstrates that the mechanism for variable binding which they advocate is fundamentally limited, and it shows how a reinterpretation of the primitive components and corresponding modifications of their system can extend the range of inference which can be supported. Our extension hinges on the basic structural modification of the network components and further modifications of the rule and fact encoding mechanism. These modifications allow the extended model to have more expressive power in dealing with symbolic knowledge as in the unification of terms across many' groups of unifying arguments.

2004

In this paper, we describe a model for reasoning using forward chaining for predicate logic rules and facts with coarse-coded distributed representations for instantiated predicates in a connectionist frame work. Distributed representations are known to give advantages of good generalization, error correction and graceful degradation of performance under noise conditions. The system supports usage of complex rules which involve multiple conjunctions. The system solves the variable binding problem using coarse-coded distributed representations of instantiated predicates without the need to decode them into localist representations. The system has performed forward reasoning successfully on the given reasoning task. It’s performance with regard to generalization on unseen inputs and its ability to exhibit fault tolerance under noise conditions is studied and has been found to give good results.

2002

The paper is an attempt to summarize the previous works of the author on integrating deductive and abductive reasoning paradigms for solving the classification task. A two-tiered reasoning and learning architecture in which Case-Based Reasoning (CBR) used both as a corrective of the solutions inferred by a deductive reasoning system and as a method for accumulating and refining knowledge is briefly described. As illustrative e~Amples the applications of the approach for problems of the case-bnsed maintenance of rnie-based systems and for case-based refinement of neural networks are presented.

Doctor of PhilosophyDepartment of Computer ScienceMajor Professor Not ListedSymbolic knowledge representation and reasoning and deep learning are fundamentally different approaches to artificial intelligence with complementary capabilities. The former are transparent and data-efficient, but they are sensitive to noise and cannot be applied to non-symbolic domains where the data is ambiguous. The latter can learn complex tasks from examples, are robust to noise, but are black boxes; require large amounts of --not necessarily easily obtained-- data, and are slow to learn and prone to adversarial examples. Either paradigm excels at certain types of problems where the other paradigm performs poorly. In order to develop stronger AI systems, integrated neuro-symbolic systems that combine artificial neural networks and symbolic reasoning are being sought. In this context, one of the fundamental open problems is how to perform logic-based deductive reasoning over knowledge bases by means of...

ABSTRACI'. The relation between logic and thought has long been controversial, but has recently influenced theorizing about the nature of mental processes in cognitive science. One prominent tradition argues that to explain the systematicity of thought we must posit syntactically structured representations inside the cognitive system which can be operated upon by structure sensitive rules similar to those employed in systems of natural deduction. I have argued elsewhere that the systematicity of human thought might better be explained as resulting from the fact that we have learned natural languages which are themselves syntactically structured. According to this view, symbols of natural language are external to the cognitive processing system and what the cognitive system must learn to do is produce and comprehend such symbols. In this paper I pursue that idea by arguing that ability in natural deduction itself may rely on pattern recognition abilities that enable us to operate on external symbols rather than encodings of rules that might be applied to internal representations. To support this suggestion, I present a series of experiments with connectionist networks that have been trained to construct simple natural deductions in sentential logic. These networks not only succeed in reconstructing the derivations on which they have been trained, but in constructing new derivations that are only similar to the ones on which they have been trained.

Lecture Notes in Computer Science, 1992

Chcl is a connectionist inference system for H orn logic which is based on the connection method and uses limited resources. This paper gives an overview of the system and its implementation.

1998

The paper is an attempt to summarize the previous works of the author on integrating deductive and abductive reasoning paradigms for solving the classification task. A two-tiered reasoning and learning architecture in which Case-Based Reasoning (CBR) used both as a corrective of the solutions inferred by a deductive reasoning system and as a method for accumulating and refining knowledge is briefly described. As illustrative e~Amples the applications of the approach for problems of the case-bnsed maintenance of rnie-based systems and for case-based refinement of neural networks are presented.

2020

This paper compares the various conceptions of “real-time” in the context of AI, as different ways of taking the processing time into consideration when problems are solved. An architecture of real-time reasoning and learning is introduced, which is one aspect of the AGI system NARS. The basic idea is to form problem-solving processes flexibly and dynamically at run time by using inference rules as building blocks and incrementally self-organizing the system’s beliefs and skills, under the restriction of time requirements of the tasks. NARS is designed under the Assumption of Insufficient Knowledge and Resources, which leads to an inherent ability to deal with varying situations in a timely manner.

We present a multi-domain computational model for symbolic reasoning that was designed with the aim of matching human performance. The computational model is able to reason by deduction, induction, and abduction. It begins with an arbitrary theory in a given domain and gradually extends this theory as new regularities are learned from positive and negative examples. At the core of the computational model is a cognitive model with bounded cognitive resources. The combinatorial explosion problem, which frequently arises in inductive learning, is tackled by searching for solutions inside this cognitive model only. By way of example, we show that the computational model can learn elements of two different domains, namely arithmetic and English grammar.