神经符号人工智能：黑盒模型时代的任务导向调研 Neuro-Symbolic Artificial Intelligence A Task-Directed Survey in the Black-Box Models Era

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Neuro-SymbolicArtificialIntelligence:

ATask-DirectedSurveyintheBlack-BoxModelsEra

GiovanniPioDelvecchio,LorenzoMolfetta,GianlucaMoro

DepartmentofComputerScienceandEngineering,UniversityofBologna,CesenaCampus

Viadell’Universit50,I-47522Cesena,Italy

{g.delvecchio,lorenzo.molfetta,gianluca.moro}@unibo.it

Abstract

Theintegrationofsymboliccomputingwithneu-ralnetworkshasintriguedresearcherssincethefirsttheorizationsofArtificialintelligence(AI).

TheabilityofNeuro-Symbolic(NeSy)methodstoinferorexploitbehavioralschemahasbeenwidelyconsideredasoneofthepossibleproxiesforhuman-levelintelligence.However,thelim-itedsemanticgeneralizabilityandthechallengesindecliningcomplexdomainswithpre-definedpatternsandruleshindertheirpracticalimple-mentationinreal-worldscenarios.Theunprece-dentedresultsachievedbyconnectionistsystemssincethelastAIbreakthroughin2017haveraisedquestionsaboutthecompetitivenessofNeSyso-lutions,withparticularemphasisontheNaturalLanguageProcessingandComputerVisionfields.

Thissurveyexaminestask-specificadvancementsintheNeSydomaintoexplorehowincorporat-ingsymbolicsystemscanenhanceexplainabil-ityandreasoningcapabilities.Ourfindingsaremeanttoserveasaresourceforresearchersex-ploringexplainableNeSymethodologiesforreal-lifetasksandapplications.Reproducibilitydetailsandin-depthcommentsoneachsurveyedresearchworkaremadeavailableat

/

disi-unibo-nlp/task-oriented-neuro-symbolic.git

.

1Introduction

“Stackedneurallayersisallweneed”.Thisstatementsum-marizesmostofthecurrentresearcheffortsintheArtificialIntelligence(AI)field,especiallyinNaturalLanguagePro-cessing(NLP)andComputerVision(CV).Theadvancementsandachievementsofthelatestneuralmodelsaremarvelous,buttheyconcealfundamentaldrawbacksregardingdataef-ficiencyandexplainability.TheneedtoresorttoNeuro-Symbolic(NeSy)componentsnaturallyarisesfromthene-cessityfortrustworthyandefficientsolutions.Thedatatypeof“thoughts”intheconnectionistapproaches—alsoknownastensors—andthehiddenunsupervisedmanipulationsofsuchinformationconstituteaphysicalbarriertohierarchicalandabstractplanning,whoseachievementcannotbereachedviamereinput-outputrelationships[

Marcus,2018

].Ifwe

18

AAAI50(20)

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IJCAI31(11)

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NeurIPS28(17)

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i

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ICLR17(10)

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EMNLP9(6)

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CVPR7(4)

o

x

ACL7(5)

ICCV2(0)

JMLR2(2)

NAACL1(1)

TACL1(1)

ConsideredDiscarded

Figure1:DistributionofNeSypeer-reviewedpapersoverthepe-riod2017-2024.Theinnermostringdelineatestheinclusioncriteria.Greyscaleslicesdenotestudiesexcludedforrelyingonblack-boxmethods,exclusivelylogicalapproaches,orbrevity,whilethecol-oredslicecomprisesthesurveyedones.Theoutermostringrepre-sentsthenumberofresearchworksfromeachselectedvenue,withexactcountsreportedinthelegend.Thenumberofpapersconsid-eredforeachtrackisenclosedinparentheses.

envisionanot-too-distantfuturewheredataavailabilityandqualitybecomecriticalconcerns,mainlyduetothepoten-tialbiasintroducedbysyntheticinformation,weurgefindingandexploringresearchpathwayswithcompositionalabilitiesweaklyrelatedtothetrainingset’sdimension[

Giunchiglia

etal.,2022

].Weupholdthatneuro-symbolicmethodscanprovideanalternativetobreakthecurse-of-dimensionalitymodernmethodologiessufferfrom.Whileeffective,spar-sityenforcementregularizationmechanisms[

Bach,2017

]re-quirestrongassumptionsaboutthenatureofthetargetdis-tribution,whichisunrealisticforthecomplexdomainsNLPandCVmodelsusuallydealwith[

Bronsteinetal.,2021

].Wearguethatsymboliccomponentscanbetheregulariza-tionforforcingmorecomplexbehaviorintoneuralmod-els.Bycombiningdata-driveninsightswithexplainable,logic-basedrepresentations,wecanachievehighergeneral-izationcapabilities[

Besoldetal.,2021

].Otherdata-drivenparadigmshavealsobeenconsidered[

Lodietal.,2010

;

Domeniconietal.,2015

].

Asthekeywords“reasoning”and“explainability”aregain-ingmoreattentioninthecommunity,wehighlightakeynotationalmisunderstandingbetweenrule-guidedandpost-

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10419

inferenceforensicstrategies.Whilebothmethodsaimtopro-videarationalebehindpredictions,theyfundamentallydifferintheirapproach.Rule-guidedmethodsconstraintheout-puttomeetspecificcriteria,whilepost-inferenceapproachesretrospectivelyreconstructplausibleinterpretablereasoningpathwaysthatledtotheresults.Wefurtherclaimthatthesetermsshouldnotbeusedtoadvocatehuman-likefacultiesbutasproxiesforgeneralizationbehaviorwithinahierar-chicalbackbonearchitecturegovernedbypredefinedrulesorcomponent-interactionschemas.

OurContributionThelackofacleardefinitionofNeSyintheAIfield,theinconsistencyinevaluationbenchmarks,andthemultitudeofuncoordinatedstudydirectionswithnocommoncomparisongroundsprimarilydrivethissurvey.Inthiswork,weconductatask-directedliteratureanalysisfo-cusingonhowNeSymethodsapplyandscaleindiverseap-plicationcontexts.Weassessthemethodologicalsoundnessofsuchapproachesandcomparethemtoblack-boxsystemsinreal-worldscenariostoidentifythecurrentlimitationsofthesestrategies.Departingfromrecentsurveysthatattempttoclassifyresearchworksalongtaxonomicalaxesornet-workarchitecturalvariations,weproposeanewmethodolog-icalapproachthatdisentanglestheseconceptualandpracti-calinconsistenciesbyprovidingacomprehensiveandcriticaloverviewofNeSysystems.Weaimtodeepentheunderstand-ingofthesehybridsystems’advantagesandinherentlimita-tions,layingthegroundworkforfutureresearchandbridgingthegapbetweenexplainabilityandperformanceinAI.

2Taxonomy

Thissectiondiscussesthestructureandsystematicrepro-duciblemethodologiesfollowedtodefineourtask-directedtaxonomyforNeSymethods.Wefurtherexaminedatasets,evaluationbenchmarks,andtheirlimitationsindelineatingfaircomparisonsacrossdifferentapproaches.Aspreviouslydiscussed,weacknowledgethenuancedusagesandincon-sistencyinthedeclinationofthetermNeSyinNLPandCVliterature,whereitisoftenmisappliedtomethodsclaimingreasoningandinterpretabilitywithoutstructuredsymbolicframeworks.Inthispaper,NeSyexclusivelyreferstoap-proachesintegratingneuralnetworkswithsymboliccompo-nentssuchassolvers,logicalrules,orstate-actionschemas.

InclusionCriteriaThissurveyaimstoinvestigateNeSysystemsfromthelastAIrevolutionin2017.Toiden-tifyrelevantresearchsystematically,weusedtheDBLPSPARQLendpointtocollectresearchpaperspublishedbe-tween2017and2024fromgeneral-purposeleadingvenuesinthosefieldswheresuchtechnologicalleaphastakenholdmore—NaturalLanguageProcessing(NLP)andComputerVision(CV).AcustomizedquerywasexecutedtoretrievepublicationsrelatedtoNeSymethodsusingthekeywords:“neuro-symbolic”,“nesy”,“rule-based”,“probabilistic-logic”,“probabilistic-reasoning”,“logic-based”,“soft-logic”,“fuzzy-logic”,“concept-learning”,“inductive-logicprogram-ming”.Figure

1

illustratesthenumberanddistributionoftheresearchworksmeetingourrequirements.Wemeticulouslyanalyzedtheresulting172papersandcategorizedthemto

identifyworksthatdeviatedfromthedesignatedNeSyfor-mulation,excludingnon-interpretablemethods,purelylogi-calapproaches,andshortpapers.Thiscollectionwasthor-oughlystudiedtoderiveapoolofresearchworksfocusingonNeSyapproachesthatintegratesymbolicreasoningwithneuralnetworks.WefurtherexploredrelevantrelatedworkstogainaprecisepictureoftheNeSyresearchlandscape.

DatasetsandBenchmarksWeanalyzedreal-worlddatasetsandbenchmarkstoensureanunbiasedcomparisonacrossmethodswhilefocusingonpracticalapplications.Thisstudyhighlightedreproducibilitychallengesintasksinvolvingsamplingoperations,suchasnegative-examplemining.WefoundsubstantialinconsistenciesontheWN18RR

1

benchmarkfordifferentresearchworksusingthesameblack-boxmodelbaselines.WefurtherspotlightanevaluationtrendintheNesyliteraturewheresyntheticdatasetsandtoytasksarespecificallytailoredforthefeaturesofthenewlyproposedmethod.Forthisreason,weconsiderthemunsuitablefordrawingconclusionsandcomparisons.InFigure

2

,welabelmostoftheidentifiedNeSytaskswiththeirrespectiveevaluationbenchmarkiftheyrespectourfairnesscriteria.Missingvaluesappearinimagegeneration,wheredifferentinstructionpromptssignificantlyimpactresults;inReinforcementLearning(RL),whereeachmethodisevaluatedoncustomtasksorgames;andincausaleffectestimation,duetooutdatedbenchmarkswithlimitedentries.

ATask-OrientedFormulationWeorganizeouranalysisbyidentifyingthreedistinctmethodologicalframeworksthattraversetheneural-symbolicresearchlandscape:(1)RuleMining,(2)RuleEnforcement,and(3)ProgramSynthesis.Withineachframework,wecategorizetechniquesbasedontheirtheoreticalgroundingandthetaskstheyaddress,focusingonhowconstraints,symbolicstructures,andinterpretableprogrammaticconstructsarerespectivelyextracted,integrated,orsynthesized.OurtaxonomyinFigure

2

isdesignedtobereadintwocomplementaryways.Atop-downperspectivehighlightshowtheseframeworksinterconnect,emphasizingsharedlogicalformalismsandlearningparadigms.Abottom-upapproachbeginswithaspecifictask,movingupwardtoidentifythemostrelevantmethodologicalfamiliesandtechniquesforthatobjective.Thisdualperspectivepreservesthefield’stheoreticalcoher-encewhilepromotingatask-directedformulationofNeSysolutions.Enablingbidirectionalexplorationbetweenrelatedmethodologiesallowsresearcherstoidentifyanalogousstrategiestorefineorexpandexistingapproachesbasedontheirobjectives.InFigure

3

weshowexamplesoftheformallanguagesemployedbyeachtheoreticalframeworkinthetaxonomy.

Inthefollowingsections,weanalyzeeachmethodologyindepth,illustratingitscoreprinciplesandhighlightingoppor-tunitiesforadvancementsinneural-symbolicintegration.

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/TimDettmers/ConvE

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DeterministicFiniteAutomata

Synthesis

Program

Rule

Enforcement

Gaming

RuleMining

DeterministicFiniteAutomata

Context-FreeGrammars

CausalEffectEstimation

LearningShaping

NaturalLogic

SemanticParsing

Reinforcement

ProbabilisticLogic

+

ReferIt3D

3DQuestionAnswering

TemporalCommonsense

Reasoning

McTACO,TIMEDIAL

FirstOrderLogic

Claim

Verification

Inference

NaturalLanguage

MultiWoZ2.1

Generation

Dialog

+

Reinforcement

LearningShielding

HornClauses

RefCOCO

FEVER/FEVEROUS

e-SNLI

Image

Manipulation

Relation

Extraction

Link

Prediction

Classification

TemporalProcessModelling

FOLIO

VerificationWeibo

Image-Text+

PredicatedDiffusion

Numerical

VisualQuestion

+

LogicalReasoning

ReasoningAnswering

CUB

DWIE

ALGEBRA

ADE20K

MIMIC-IV

WN18RR

NeuralNetworkVerification

GTSRB

Figure2:Task-DirectedNeSyTaxonomy.WeorganizethemostrelevanttaskfamiliesbyclassifyingeachaccordingtoapplicableNeSy

techniquesandgroupingthemintothreemacro-categories:(1)RuleMining,(2)RuleEnforcement,and(3)ProgramSynthesis.Wealsolabelthemostcommonlyuseddatasetstohighlighttheirroleinreal-worldbenchmarkingandmodelevaluation.Tasksareorganizedfrombottomtotopandfromlefttorightwithineachcategory,mirroringthesurvey’sconceptualprogression.

3Rule-Miningtechniques

Neuro-Symbolictechniquesemployrule-miningasacoremethodologyformodelconstruction,focusingonextract-inginterpretablerulesfromdiverseinputdata.Thecom-putationalcomplexityofruleextractiondirectlycorrelateswiththechosenformalspecificationlanguage.Hornclauseapproachesexhibitthehighestcomplexity,requiringmatrixrepresentationsforgroundatomtruthvalues.NaturalLogicframeworksshowmoderatecomplexity,combininglinguis-ticpreprocessingwithquestion-answeringforentityandop-eratorextraction.DeterministicFiniteAutomata(DFAs)presentthelowestcomplexity,leveragingoperationaltraceswithSAT-solvingforrulelearning.

3.1HornClauses

HornClauses(HCs),afundamentalcomponentoflogicpro-gramming,provideastructuredframeworkforrule-basedreasoning.Definedasdisjunctionsofliteralswithatmostonepositiveliteralastheclausehead,HCsenablelogicalin-ferenceacrossvariousdomains.

TemporalpointprocessmodelingreliesonHC-basedrea-soningtocaptureeventdependencies,whichisparticularlycrucialinfieldssuchasmedicineandautonomousdriving,wheresuddenchangesinconditionscanhavesevereconse-quences.[

Yangetal.,2024

]introducedaNeSyruleinductionmethodthatleveragesasequentialcoveringalgorithmandacustomattentionmechanismtoextractHCs.Whiledemon-stratingscalability,trustworthiness,andstrongperformanceoverexistingmodels,itsabilitytocaptureincreasinglycom-plexrulesremainsanopenresearchquestion.

TheInductiveLogicProgramming(ILP)paradigmauto-matesthediscoveryofHC-basedrules,supportinggeneral-izedreasoningandinferenceoverstructureddata.Inthecon-textofextractingrulesfromstructureddataliketablesandgraphs,ILPseekstoidentifymissingconnectionsbetweenentitiesbyuncoveringpatternsinexistingrelationships.DFORL[

Gaoetal.,2024

],arecentlightweightmethodforefficientruleextraction,introducesadepth-limitedbreadth-firstsearchforneighborhoodextraction.Thisproposition-alizationtechniqueconvertsrelationalfactsintovectorrep-resentationssuitableforneuralnetwork-basedlearningandappliessyntacticconstraintstoreducetherulesearchspace.

Byintegratingauxiliarymatricesandcurriculumlearning,DFORLuncovershiddenpredicatesandenhancestheeffi-ciencyandprogressionofthetrainingprocess.Althoughthisapproachdemonstratespotentialinreal-worldapplica-tionssuchasdrugdesign[

Kingetal.,1995

],itsperformanceontheWN18RRlinkpredictionbenchmarkremainsincon-sistent.Thisvariabilityprimarilystemsfromthedataset’sdesign,whichomitsinverserelationsinthetestset,com-plicatingdirectcomparisonswithbaselinemethodsandsug-gestingthatmethodslikeDFORLcouldbenefitfromincor-poratingnegationinrulebodiestoenhancethemodel’sabil-itytohandlehigher-aritypredicates.NCRL,acomplemen-taryapproachby[

Chengetal.,2023

],focusesonrulecom-positionality,samplingalternativepathsbetweenconnectednodestoconstructHornclauses.Thismethodemploysanit-erativealgorithmcombininganRNN-basedselectionprocesswithanattentionmechanism,aimingtomaximizethelike-lihoodthatheadpredicatescanbereconstructedfromsam-pledpathpredicates.Byleveragingpredicateembeddings,NCRLoutperforms[

Gaoetal.,2024

]onWN18RR,mainlyduetoitshigherabilitytoinfersemanticrelationshipswheninverserelationsaremissing.Itsstrongperformanceinlow-dataregimesandrapidconvergenceonGPUmakesNCRLacompellingalternativeforthesametask.

Appliedtotabulardata,InductiveLogicProgrammingfoundationsareleveragedinFold-SE[

WangandGupta,

2024

]toextractinterpretablelogicalrulesforsupervisedtabularclassification.Designedtohandlebothcategoricalandnumericaldatawithminimalpreprocessing,itscalesef-ficientlytolargedatasetswhilepreservingrulecoherence.Followingasequentialcoveringstrategy,Fold-SEiterativelyrefinesrulesbyoptimizingamodifiedGiniImpuritymet-rictoenhanceclassificationperformance.BuiltuponFold-SE,NeSyFOLD[

Padalkaretal.,2024

]adoptsILPonex-tractedhighlevelfeaturesforanimageclassificationtask.NeSyFOLDderivesrulesfrombinaryactivationmaskspro-ducedbyConvolutionalNeuralNetworks(CNNs),assign-ingsemanticlabelstokernelsposthoc.ItsrelianceonCNNarchitectures—extendedandoutperformedbymoderntransformer-basedmodels—constrainsitseffectiveness,andtheexclusionofexceptionpredicatesinsemanticlabelingfur-therrestrictsitsrepresentationalcapacity.

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Inthetextualdomain,Document-levelRelationExtrac-tion(DocRE)isasupervisedlearningtaskthatidentifiesre-lationsr(h,t)betweenentities,whererrepresentsthere-lation,histheheadentity,andtisthetailentity.BothNeSymodelsandblack-boxapproacheshavebeenevalu-atedonDWIE,awidelyrecognizedbenchmarkforDocRE.JMLR,anovelframeworkintroducedin[

Qietal.,2024

],integratesDocREwithruleextractionthroughresidualcon-nections.Thisapproachcomputesrulesupportasaweightedsumofatomsupports,facilitatingtheimplementationofsoft-proofmechanismsthatcombinerelationsintoHCs.[

Jainet

al.,2024

]adoptedanalternativeformulation,treatingDocREasaknowledgebaselinkpredictiontaskandutilizingtheblack-boxmodelDocRE-CLiPtoinferrelationalstructures.FedNSL,introducedin[

Xingetal.,2024

],extendsNeSymethodstoafederatedlearningsettingforDocRE,achiev-ingperformancebetweenthatofDocRE-CLiPandJMLR.Whileitsevaluationofreal-worlddatasetsremainslimitedtoDWIE,theframeworkdemonstratesthepotentialforprivacy-preservingalgorithms.Byleveragingvariationalexpectationmaximization,itefficientlyconstrainstherulesearchspace,reducingtrainingroundswhilemaintainingcompetitiveper-formance.Acomparativeevaluationofthesemethods—asshowninTable

1

—indicatesthatJMLRsignificantlyout-performsDocRE-CLiPonDWIEwhileachievingsimilarre-sultsonotherbenchmarks,highlightingtheadvantagesofrule-basedreasoningincapturingcomplexmulti-sentencere-lationships.However,JMLRdoesnotexplicitlyincorporateexternalknowledge,afeaturemorenaturallyintegratedintoknowledge-base-drivenmethods.

3.2NaturalLogic

NaturalLanguageInference(NLI)determinesentailmentre-lationsbetweenapremiseandahypothesisusingformalop-eratorssuchasequivalence(=)andforwardentailment(c).[

Fengetal.,2022

]proposedatransformer-basedNeSymodelthatintegratedGPT-2withreinforcementlearningforop-eratorcompositionandintrospectiverevisionusingWord-Net.ThisapproachoutperformsbaselineslikeBERTonmostbenchmarksbutremainssensitivetolinguisticnoise,suchasadverbsandprepositionalphrasemodificationsinbench-markdatasets.QA-NatVer[

Alyetal.,2023

]extendedthisframeworktoclaimverification,constructingproofsthroughsentencealignment,operatorassignment,andacustomDFA.AsshowninTable

1

,QA-NatVerhighlightsthetrade-offbe-tweenNeSymodels’explainabilityandperformance,withanotableaccuracydropduetoitsrelianceonasmalltrainingset.Itsblack-boxcounterpart,SFAVEL[

Bazagaetal.,2024

],overcomesthislimitationusingself-supervisionanddistilla-tiontoremovetheneedforlabeleddata.TabVer[

Alyand

Vlachos,2024

]furtherextendedNLItotabularclaimver-ificationbyincorporatingnumericalreasoning,recognizingequivalences,alongsidepragmaticreasoningthroughdeter-ministicrules.WhileachievingstrongresultsonFEVER-OUSdatasets,itstruggleswithexactnumericalmatching,un-derscoringongoingchallengesinadaptingNeSymethodstolessrigidreasoningtasks.

3.3DeterministicFiniteAutomaton

DeepQ-learninghasproveneffectiveinreinforcementlearning(RL),particularlyintasksthatrequiresequen-tialdecision-makingandstructuredexploration.Traditionalblack-boxmethodsstrugglewithenvironmentsliketheAtariclassicgame“Montezuma’sRevenge”,wheresuccessde-pendsoncomplexinteractionsbetweenobjectsandpreciseroomnavigation.ADeterministicFiniteAutomatonprovidesastructuredwaytomodelsequentialdependenciesbyrep-resentingstatetransitionsthroughafinitesetofrules.Thisformalismcanbeleveragedtoguideexplorationandim-provedecision-makingincomplexRLenvironments.Lever-agingthisformalism,[

Hasanbeigetal.,2024

]proposesadeepQ-learningframeworkaugmentedwithDFAsynthesistoenhanceexplorationefficiencyandpolicyoptimization.Bystructuringlearnedbehaviorsasstatetransitions,thisap-proachenablesmoreeffectivereasoningoversequentialde-pendencies.Withinthisframework,theRLalgorithmgener-atesexplorationtracesthatcapturesequencesofstate-actionpairsalongsiderewardestimates.ThesetracesinformaDFAsynthesismodule,whichformulateslogicalconstraintsandemploysaSATsolvertoconstructaminimal-stateDFAen-codingtheagent’slearnedbehavior.Byleveragingthisstruc-turedrepresentation,thedeeplearningmodulerefinespolicytransitions,optimizingstate-actionmappingsanditerativelyimprovingdecision-makingwithintheRLprocess.Experi-mentsdemonstratethattheframeworkachievesfasterconver-genceintasksrequiringsequentialplanningandobjectinter-actions,outperformingconventionalmodelsthatfailtocon-verge.Integratingexpert-designedDFAsfurtherenhancesef-ficiencybyeliminatingtheinitialexplorationphaseandexpe-ditingtraining.Futureresearchmayextendthisapproachbe-yondgamingandinvestigateusingmoreexpressiveautomata,suchasPushdownAutomata,tomodelhierarchicalmemorystructures[

Sipser,1997

].

4Rule-EnforcementTechniques

Thissectionpresentspromisingmethodologiesforenforcingconstraintsintheformofrulesoversystemsforvariousappli-cationpurposes.Theseconstraintscanbeenforcedthroughtailorednetworksorbyregularization.

4.1First-Order-Logic

IntegratingFirst-OrderLogic(FOL)rulesintoconstrainedimagegenerationhasbeenexploredtoenhancecontrolla-bilityandtrustworthiness.[

SueyoshiandMatsubara,2024

]introducedapioneeringapproachthatextractsFOLcon-straintsfromtextusingdependencyparsingandtranslatesthemintoequationsgoverningtheintensityofattentionmaps.Ratherthanmininglogicalconstraintsfromlargedatasets,thismethodemploysaregularizationstrategy—awell-establishedpracticeinneuro-symbolicreasoning—asdemonstratedbylaterworksinthissurvey[

Caietal.,2022

;

Pryoretal.,2023

].Inthisapproach,thelogicalstructureisnotinferredfromdatabutexplicitlyimposedthroughaspe-cializedlossfunctionthatguidesthegenerationprocess.No-tably,thismethodnativelysupportslogicalquantifiers,which

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NaturalLanguageInference

Thekid

doesnotlovetabletennis

≡≡c

Thekid

sports

doesnotlike

SemanticParsing

SubjectsAllrectangleshavefour-sides

PredicatesAll ObjectsAll

four-sidedthingsareshapesrectanglesareshapes

HornClauses/FirstOrderLogic

Allrectangleshavefoursides→FourSided(x)←Rectangle(x)

/

Allrectangleshavefoursides→∀xFourSided(x)←Rectangle(x)

ProbabilisticLogic

I'malmostsurethatallrectangleshavefoursides

→

0.9:FourSided(x)←Rectangle(x)

DeterministicFiniteAutomaton

run

start

idle

ContextFreeGrammars

Wellformedparentheses:{λ,(),(()),...,(n)n}R1:S→(S)Terminalsymbols:{"(",")",λ}

R2:S→λNonterminalsymbols:{S}

(λistheemptystring)

Figure3:Overviewoftheintermediateformallanguagesemployedbyeachtaxonomymethod.

allowforformulatingmorepreciseandinterpretablecon-straints.QualitativeanalysessuggestthatincorporatingFOLconstraintsinimagegenerationsignificantlyenhancescon-tentfidelity,makingthisapproachhighlyrelevantforapplica-tionslikechatbotsandautomatedcontentcreation.However,theabsenceofacountingmechanismpreventsconstrainten-forcementonrepeatedentities(e.g.,“ablackdogandawhitedog”),whileabiastowardprototypicalexampleslimitsflexi-bility.Visualconceptlearningandsemanticparsingcouldbeincorporatedtoaddressthesechallenges[

Maoetal.,2019

].

Reasoningoverimagesisessentialfordetectingmulti-modalmisinformation,wheredeceptionstemsfromthein-terplayoftextandvisuals.Whiletraditionalblack-boxap-proacheshaveachievedhighaccuracyinthisdomain,thelackofinterpretabilityremainsamajorlimitation.[

Dongetal.,

2024

]introducedaNeSypipelinethatenhancestransparencybyintegratinglogicalreasoningintotheclassificationpro-cess.Usingtwoencodermodels,themodelextractspatternsfrombothmodalitiesandemploysateacher-studentnetworktoestimateprobabilitiesforthreelatentvariables:imagema-nipulation,cross-modalinconsistency,andimagerepurpos-ing.AuniqueFOLruleclassifiesasampleasfakeifanyofthethreevariablesholdtrue.Table

1

showsthismethodtrail-ingitsblack-boxcounterpartbyafewpoints,like