Abstract
Connectionist attention to variables has been too restricted in two ways. First, it has not exploited certain ways of doing without variables in the symbolic arena. One variable-avoidance method, that of logical combinators, is particularly well established there. Secondly, the attention has been largely restricted to variables in long-term rules embodied in connection weight patterns. However, short-lived bodies of information, such as sentence interpretations or inference products, may involve quantification. Therefore short-lived activation patterns may need to achieve the effect of variables. The paper is mainly a theoretical analysis of some benefits and drawbacks of using logical combinators to avoid variables in short-lived connectionist encodings without loss of expressive power. The paper also includes a brief survey of some possible methods for avoiding variables other than by using combinators.
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References
BarndenJ.A. (1989), ‘Neural-net implementation of complex symbol-processing in a mental model approach to syllogistic reasoning’. In Procs. 11th Int. Joint Conf. on Artificial Intelligence, pp. 568–573. San Mateo, CA: Morgan Kaufmann.
BarndenJ.A. (1991), ‘Ecoding complex symbolic data structures with some unusual connectionist techniques’, Advances in Connectionist and Neural Computation Theory, Vol. 1: High Level Connectionist Models, pp. 180–240. Norwood, N.J.: Ablex Publishing Corp.
BarndenJ.A. (1992), ‘Connectionism, generalization and propositional attitudes: a catalogue of challenging issues’. In J.Dinsmore (ed.), The Symbolic and Connectionist Paradigms: Closing the Gap. Hillsdale, N.J.: Lawrence Erlbaum. pp. 149–178.
Barnden, J.A. (1994), ‘Complex symbol-processing in Conposit, a transiently localist connectionist architecture’. In R. Sun & L. Bookman (Eds.), Computational Architectures for Integrating Neural and Symbolic Processes. Kluwer.
BarndenJ.A. (1995), ‘High-level reasoning, computational challenges for connectionism, and the Conposit solution’, Applied Intelligence 5 (2), pp. 1–33.
BarndenJ.A. & SrinivasK. (1991), ‘Encoding techniques for complex information structures in connectionist systems’, Connection Science 3 (3), pp. 263–309.
BarndenJ.A. & SrinivasK. (1992a) ‘Overcoming rule-based rigidity and connectionist limitations through massively-parallel case-based reasoning’, Int. J. Man-Machine Studies 36, pp. 221–246.
BarndenJ.A. & SrinivasK. (1992b). ‘Working memory variables, logical combinators and systematicity’, Memoranda in Computer and Cognitive Science, No. MCCS-92-245, Computin Research Laboratory, New Mexico State University, Las Cruces, NM 88003.
BarndenJ.A. & SrinivasK. (1995), ‘Combinators for Connectionism: Quantification. Substitution and Unification without Variables’, Memoranda in Computer and Cognitive Science, No. MCCS-95-286, Computing Research Laboratory, New Mexico State University, Las Cruces, NM 88003.
BlankD.S., MeedenL.A. & MarshallJ.B. (1992), ‘Exploring the symbolic/subsymbolic continuum: a case study of RAAM’. In DinsmoreJ. (Ed.), The Symbolic, and Connectionist Paradigms: Closing the Gap, pp. 113–148. Hillsdale, N.J.: Lawrence Erlbaum.
ChalmersD.J. (1990), ‘Syntactic transformations on distributed representations’, Connection Science 2 (1&2), pp. 53–62.
ChapmanD. & AgreP.E. (1987), ‘Abstract reasoning as emergent from concrete activity’. In M.P.Georgeff & A.L.Lansky (Eds.), Reasoning about Actions and Plans. Los Altos, CA: Morgan Kaufmann.
ChrismanL. (1991). ‘Learning recursive distributed representations for holistic computation’, Connection Science, 3 (4), pp. 354–366.
CurryH.B. & FeysR. (1958), Combinatory Logic. Amsterdam: North-Holland.
DavisE. (1990), Representations of Commonsense Knowledge. San Mateo, CA: Morgan Kaufmann.
DyerM.G. (1991), ‘Symbolic NeuroEngineering and natural language processing: a multilevel research approach’, In J.A.Barnden & J.B.Pollack (Eds.), Advances in, Connectionist and Neural Computation Theory, Vol. 1 Norwood, N.J.: Ablex Publishing Corp. pp. 32–86.
DyerM.G., FlowersM. & WangY.A. (1988), Weight-matrix = pattern of activation: encoding semantic networks as distributed representations in DUAL, a PDP architecture. Tech. Report UCLA-AI-88-5, Department of Computer Science, University of California, Los Angeles, CA.
FodorJ.A. & PylyshynZ.W. (1988), ‘Connectionism and cognitive architecture: A critical analysis’. In S.Pinker, & J.Mehler (Eds.), Connections and Symbols. Cambridge, MA: MIT Press and Amsterdam: Elsevier.
HadleyR.F. (1993b), ‘Connectionism, explicit rules, and symbolic manipulation.’, Minds and Machines 3 (2), pp. 183–200.
HadleyR.F. (1993b), ‘Compositionality and systematicity in connectionist language learning’, CSS-IS TR 93-01, Centre for Systems Science, Simon Fraser University, Burnaby, B.C.
HarrisC.L. & ElmanJ.L. (1989), ‘Representing variable information with simple recurrent networks’. In Proc Eleventh Annual Conf. of the Cognitive Science Society, pp. 635–642. Hillsdale, N.J.: Lawrence Erlbaum.
HintonG.E. (1990), ‘Mapping part-whole hierarchies into connectionist networks’, Artificial Intelligence 46 (1–2), pp. 47–75.
HölldoblerS. (1990), ‘A structured connectionist unification algorithm’, In Procs. 8th National Conf. on Artificial Intelligence (AAAI-90), pp. 587–593. Menlo Park, CA: AAAI Press.
Hudak, P. & Goldberg, B. (1985), ‘Efficient distributed evaluation of functional programs using serial combinators’, IEEE Trans on Computers C-34 (10), pp. 831–839.
Johnson-LairdP.N. (1983), Mental Models: Towards a Cognitive Science of Language, Inference and Consciousness. Cambridge, Mass. Harvard University Press.
Johnson-LairdP.N. & ByrneR.M.J. (1991), Deduction. Hove, U.K.: Lawrence Erlbaum.
LangeT.E. & DyerM.G. (1989), ‘High-level inferencing in a connectionist network’, Connection Science 1 (2), pp. 181–217.
MiyataY., SmolenskyP. & LegendreG. (1993), ‘Distributed representation and parallel processing of recursive structures’, In Procs. 15th Annual Conf. of the Cognitive Science Society. Hillsdale, N.J.: Lawrence Erlbaum.
NiklassonL. & vanGelderT. (1994), ‘Can connectionist models exhibit non-classical structure sensitivity?’ In Procs. Sixteenth Annual Conference of the Cognitive Science Society, pp. 664–669. Hillsdale, N.J.: Lawrence Erlbaum.
Peyton JonesS.L. (1987), The Implementation of Functional Programming Languages. Englewood Cliffs, N.J.: Prentice-Hall.
Peyton Jones, S.L., Clack, C. & Salkid, J. (1989), ‘High performance parallel graph reduction’. In Proceedings of PARLE '89, Parallel Architectures and Languages Europe, pp. 193–206. Springer-Verlag.
PinkasG. (1992), ‘Constructing proofs in symmetric networks’. In J.E.Moody, S.J.Hanson, R.P.Lippmann (Eds.), Advances in Neural Information Processing Systems, pp. 217–224. San Mateo: Morgan Kaufmann.
PinkerS. & PrinceA. (1988), ‘On language and connectionism: analysis of a parallel distributed processing model of language acquisition’. In S.Pinker & J.Mehler (Eds.), Connections and Symbols, Cambridge, Mass.: MIT Press. (Reprinted from Cognition, 28, 1988).
PlateT. (1991), ‘Holographic reduced representations: convolution algebra for compositional distributed representations’. In Procs. 12th Int. Joint Conf. on Artificial Intelligence (Sydney, Australia, Aug, 1991), pp. 30–35. San Mateo: Morgan Kaufmann.
PollackJ.B. (1990), ‘Recursive distributed representations’, Artificial Intelligence 46 (1-2), pp. 77–105.
St.JohnM.F. & McClellandJ.L. (1990), ‘Learning and applying contextual constraints in sentence comprehension’, Artificial Intelligence 46 (1–2), pp. 217–257.
Schönfinkel, M. (1924), ‘Über die Bausteine der mathematischen Logik’, Math Ann. 92, p. 305.
ShastriL. & AjjanagaddeV. (1993), ‘From simple associations to systematic reasoning: a connectionist representation of rules, variables, and dynamic bindings using temporal synchrony’, Behavioral and Brain Sciences 16 (3), pp. 417–494.
SmolenskyP. (1988). ‘On the proper treatment of connectionism’, Behavioral and Brain Sciences 11, 1–74.
SunR. (1990), Integrating Rules and Connectionism for Robust Commonsense Reasoning. New York: Wiley.
TouretzkyD.S. (1990), ‘BoltzCONS dynamic symbol structures in a connectionist network’, Artificial Intelligence 46 (1–2), pp. 5–46.
TurnerD.A. (1979), ‘A new implementation technique for applicative languages’, Software Practice and Experience 9, pp. 31–49.
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This work was supported in part by grant AFOSR-88-0215 from the Air Force Office of Scientific Research, to Barnden, and grant NAGW-1592 under the Innovative Research Program of the NASA Office of Space Science and Applications, to Barnden and C.A. Fields.
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Barnden, J.A., Srinivas, K. Quantification without variables in connectionism. Mind Mach 6, 173–201 (1996). https://doi.org/10.1007/BF00391285
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DOI: https://doi.org/10.1007/BF00391285