README⤓ .txt 2026-08-19T232029.000 000000000009192 Logics for representing knowledge and drawing inferences from it, especially the defeasible, nonmonotonic, and ontological reasoning that formal knowledge systems require. The concern is representation and inference for artificial reasoning, not the epistemic modality itself.
Abductive Logic⤓ .md 2026-08-20T062448.000 000000000036664 Peirce introduced abduction (late 19th c.). Formalized in AI by Pople, Poole (1970s-80s). Inference to best explanation. Given observation and theory, find hypothesis explaining it. Foundation for diagnosis, planning, theory formation.
Abstract Argumentation⤓ .md 2026-08-20T065330.000 000000000045464 Phan Minh Dung introduced abstract argumentation frameworks (1995). Arguments are abstract entities; the focus is on attack relations and acceptable sets. Unified view subsuming logic programming, default logic, and other non-monotonic systems. Foundation for computational argumentation in AI, law, and multi-agent systems.
Action Languages⤓ .md 2026-08-20T065108.000 000000000036184 Gelfond and Lifschitz introduced action language A (1993). Subsequent: B, C, AL, and others. Formalisms for describing action effects. Connects to situation calculus and event calculus. Foundation for planning and reasoning about change.
Adaptive Logic⤓ .md 2026-10-22T165042.936 000000000000848 Diderik Batens and the Ghent Centre for Logic and Philosophy of Science developed adaptive logics from the early 1980s, starting with inconsistency-adaptive systems that reason as classically as a possibly inconsistent premise set allows while localizing the damage. The programme was consolidated into the "standard format" — a triple of lower limit logic, abnormality set and strategy — in Batens, "A general characterization of adaptive logics" (2001), and "A universal logic approach to adaptive logics" (2007), which prove the metatheory once for every logic presented in the format rather than case by case.
Answer Set Programming⤓ .md 2026-08-20T062834.000 000000000042792 Emerged from logic programming semantics: stable model semantics (Gelfond & Lifschitz, 1988) and well-founded semantics. Answer Set Programming (ASP) as a paradigm crystallized in the 1990s-2000s. Non-monotonic, supports negation as failure, defaults, and constraints. Implemented in efficient solvers: Clingo, DLV, WASP.
ASPIC+⤓ .md 2026-08-20T065850.000 000000000044584 Henry Prakken (2010), generalizing the ASPIC framework of Amgoud et al.; developed with Sanjay Modgil (2013, 2018). A general framework for structured argumentation that builds Dung argumentation frameworks from an underlying logical language, rules, and preferences, with rationality guarantees.
Assumption-Based Argumentation⤓ .md 2026-08-20T065749.000 000000000037512 Bondarenko, Dung, Kowalski, Toni (1997). Structured argumentation. Arguments from assumptions. Rules derive conclusions. Attacks via contraries. Foundation for logic-based argumentation.
Autoepistemic Logic⤓ .md 2026-08-20T013937.000 000000000036328 Robert Moore introduced autoepistemic logic (1985) to formalize reasoning about one's own beliefs. An ideally rational agent reasoning about what they know and don't know. Non-monotonic: "I don't believe P, so P is probably false." Related to default logic but based on belief rather than defaults. Foundation for introspective reasoning in AI.
Belief Revision⤓ .md 2026-08-20T073446.000 000000000043832 Alchourrón, Gärdenfors, and Makinson introduced AGM theory (1985). Formalizes rational belief change. Three operations: expansion (adding belief), contraction (removing belief), revision (adding belief while maintaining consistency). Foundational for AI knowledge base maintenance and epistemology.
Bipolar Argumentation⤓ .md 2026-10-22T090028.000 000000000043328 Cayrol and Lagasquie-Schiex (2005) added a second, positive relation to Dung's frameworks, so that one argument may support another as well as attack it, on the ground that pro-and-con reasoning is not reducible to attack alone. What support means was left open, and later work fixed it in incompatible ways: deductive support (Boella, Gabbay, van der Torre and Villata 2010), necessary support (Nouioua and Risch 2010), evidential support (Oren and Norman 2008). Each reading yields its own notion of complex attack and its own semantics.
Cardinal Direction Calculi⤓ .md 2026-10-22T090631.000 000000000072136 Frank ("Qualitative spatial reasoning about cardinal directions", 1991) gave the two point-based schemes — cone-based and projection-based — that everything since has been a correction of. Ligozat, "Reasoning about cardinal directions" (Journal of Visual Languages and Computing 9, 1998), supplied the algebraic treatment of the projection-based case. Goyal and Egenhofer ("The direction-relation matrix", 1997; the journal version "Cardinal directions between extended spatial objects" was long cited as in press at IEEE TKDE but never appeared) replaced points with regions and produced the Cardinal Direction Calculus, the model the field now means by the name. Skiadopoulos and Koubarakis ("Composing cardinal direction relations", Artificial Intelligence 152, 2004) found that Goyal and Egenhofer's composition method fails on some inputs and gave a correct one; Liu, Zhang, Li, and Ying (AIJ 174, 2010) settled the complexity.
Circumscription⤓ .md 2026-08-20T061720.000 000000000042544 John McCarthy introduced circumscription (1980) as a formalization of the closed-world assumption and non-monotonic reasoning. "Minimize the extension of abnormality predicates." A form of default reasoning via model-theoretic minimization. Influential in AI knowledge representation alongside default logic and autoepistemic logic.
Commitment Logic⤓ .md 2026-08-20T071511.000 000000000051800 Hamblin (1970) introduced commitment stores into formal dialectic, replacing an account of dialogue in terms of what speakers believe with one in terms of what they have publicly undertaken. Walton and Krabbe (1995) built the systematic theory, classifying dialogue types — persuasion, negotiation, inquiry, deliberation, information-seeking, eristic — and giving each its own commitment rules. Singh (1998) and Fornara and Colombetti (2002) carried the idea into multi-agent systems in response to a specific problem: the mentalistic semantics of KQML and FIPA-ACL define a message by the sender's beliefs and intentions, which no observer can check.
Conceptual Graphs⤓ .md 2026-10-22T224233.000 000000000061672 John F. Sowa, "Conceptual Graphs for a Data Base Interface" (IBM Journal of Research and Development 20(4), 1976, 336–357), then the defining book Conceptual Structures: Information Processing in Mind and Machine (Addison-Wesley, 1984), presenting the graphs as a synthesis of Peirce's existential graphs and the semantic networks of AI (see Existential Graphs.md). The mathematical consolidation is due to the Montpellier school: Michel Chein and Marie-Laure Mugnier, "Conceptual Graphs: Fundamental Notions" (Revue d'Intelligence Artificielle 6(4), 1992, 365–406), and their book Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs (Springer London, 2009). The Conceptual Graph Interchange Format CGIF is Annex B of ISO/IEC 24707, Common Logic (2007; second edition 2018).
Datalog⤓ .md 2026-08-20T062806.000 000000000048144 Datalog crystallized out of the deductive-database research that followed Gallaire and Minker's Logic and Data Bases workshops (1977 onward), the name being due to David Maier: take logic programming, delete function symbols, and what remains is a query language over a finite database. Chandra and Harel (1985) analysed the expressive power of Horn-clause queries, Bancilhon, Maier, Sagiv and Ullman (1986) gave the magic-sets transformation that makes bottom-up evaluation goal-directed, and Apt, Blair and Walker (1988) fixed the semantics of stratified negation. The language was revived in the 2000s for static program analysis, network protocols and ontology-based data access.
Default Logic⤓ .md 2026-08-20T061538.000 000000000042624 Raymond Reiter introduced default logic (1980). A formalization of non-monotonic reasoning: conclusions that hold "by default" and can be retracted when contradicting information arrives. Part of the broader study of non-monotonic logics (circumscription, autoepistemic logic). Models commonsense reasoning where we reason with incomplete information.
Defeasible Logic⤓ .md 2026-08-20T061822.000 000000000042696 Donald Nute developed defeasible logic (1980s-1994). Practical non-monotonic reasoning with explicit rules and priorities. Designed for efficient computation unlike some other non-monotonic logics. Used in legal reasoning, business rules, and agent systems. Related to but distinct from default logic and argumentation.
Description Logic ALC⤓ .md 2026-08-20T060739.000 000000000039288 Schmidt-Schauß and Smolka, "Attributive concept descriptions with complements" (Artificial Intelligence, 1991). Attributive Language with Complements; the basis of OWL (W3C, 2004) and of the SH family of extensions. Core description logic. Basis for OWL. Decidable reasoning about concepts and roles.
Description Logic SROIQ⤓ .md 2026-10-22T165042.936 000000000000920 Horrocks, Kutz, Sattler (2006). Foundation for OWL 2 DL. Extends ALC with: role hierarchies, transitivity, nominals, inverse, qualified cardinality. Most expressive decidable DL in wide use.
Description Logic⤓ .md 2026-10-22T090936.000 000000000046368 Evolved from semantic networks and frame systems (1970s-80s). KL-ONE (Brachman & Schmolze, 1985) was influential. The "description logic" family formalized with attention to computational complexity. Foundation for OWL (Web Ontology Language) and the Semantic Web. Balances expressiveness with decidability.
DL-Lite⤓ .md 2026-10-22T090030.000 000000000036592 Calvanese et al. (2007). Lightweight description logic. Polynomial query answering. Foundation for OWL 2 QL. Designed for databases with ontologies.
Dynamic Epistemic Logic⤓ .md 2026-08-20T014831.000 000000000035816 Plaza introduced public announcement logic (1989). Baltag, Moss, and Solecki generalized to action models (1998). Van Benthem unified dynamic and epistemic traditions. Combines epistemic logic with dynamic updates. Models how knowledge changes through communication and observation.
EL Description Logic⤓ .md 2026-08-20T061014.000 000000000047192 EL grew from the observation that the intractability of description logics comes from disjunction and negation rather than from existential restriction. Baader, "Terminological cycles in a description logic with existential restrictions" (2003), showed that subsumption stays polynomial even with cyclic terminologies; Brandt (2004) extended tractability to general concept inclusions and role hierarchies; Baader, Brandt and Lutz, "Pushing the EL Envelope" (IJCAI 2005), fixed the extension EL++ and mapped the boundary beyond which tractability fails. The design was vindicated in practice by SNOMED CT, and EL++ became the OWL 2 EL profile (W3C, 2009).
Epistemic Description Logic⤓ .md 2026-08-20T061317.000 000000000033752 Donini et al. (1992). Combine DL with epistemic operators. Knowledge about ABox: K. Introspection: what is known. Foundation for ontology-based epistemic reasoning.
Epistemic Logic⤓ .md 2026-08-20T012257.000 000000000040408 Jaakko Hintikka's Knowledge and Belief (1962) established epistemic logic as a formal discipline. Builds on modal logic with knowledge and belief as modalities. Extended to multi-agent systems by Halpern, Moses, and others (1980s-1990s). Common knowledge formalized by David Lewis (1969) and Aumann (1976).
Equilibrium Logic⤓ .md 2026-08-20T063022.000 000000000038712 Pearce (1996). Logic programming semantics. Here-and-there logic. Answer sets as equilibria. Foundation for answer set programming.
Event Calculus⤓ .md 2026-08-20T064901.000 000000000039848 Kowalski and Sergot introduced Event Calculus (1986). Formalism for reasoning about events and their effects. Alternative to Situation Calculus. Based on time points and fluents. Better handles continuous time and narrative.
Existential Rules⤓ .md 2026-10-22T180154.561 000000000000872 The rules are the tuple-generating dependencies of 1970s database theory, and the chase that saturates them comes from Maier, Mendelzon and Sagiv, "Testing Implications of Data Dependencies" (ACM TODS 4(4): 455–469, 1979), and Aho, Beeri and Ullman, "The Theory of Joins in Relational Databases" (ACM TODS 4(3): 297–314, 1979). Beeri and Vardi, "The implication problem for data dependencies" (ICALP 1981), and Chandra, Lewis and Makowsky (STOC 1981) proved the associated inference problems undecidable. The rereading as an ontology language came in three bodies of work: data exchange (Fagin, Kolaitis, Miller and Popa, "Data exchange: semantics and query answering", Theoretical Computer Science 336(1): 89–124, 2005), the Datalog± programme (Calì, Gottlob and Lukasiewicz, "A general Datalog-based framework for tractable query answering over ontologies", PODS 2009; Calì, Gottlob, Lukasiewicz, Marnette and Pieris, LICS 2010), and the ∀∃-rules of the graph-based tradition (Baget, Leclère and Mugnier, "Walking the decidability line for rules with existential variables", KR 2010).
Fluent Calculus⤓ .md 2026-10-22T165042.936 000000000000856 Thielscher developed Fluent Calculus (1999). Evolution of Situation Calculus. States as explicit objects containing fluents. Addresses frame problem via state update axioms. Foundation for FLUX agent programming system.
Formal Concept Analysis⤓ .md 2026-08-20T072509.000 000000000044192 Wille (1982). Lattice-based knowledge. Objects and attributes. Concept hierarchies. Foundation of conceptual knowledge.
Frame Logic⤓ .md 2026-10-22T090033.000 000000000037888 Kifer, Lausen, Wu (1995). Object-oriented knowledge representation. Frames with logic. Methods and inheritance. Foundation for F-logic systems.
Fuzzy Logic⤓ .md 2026-08-20T065009.000 000000000044248 Lotfi Zadeh introduced fuzzy sets (1965) and fuzzy logic for reasoning under vagueness. Petr Hájek provided mathematical foundations (Metamathematics of Fuzzy Logic, 1998). Practical applications in control systems, AI, and decision making. Distinct from probability: fuzziness is about vague boundaries, not uncertain events.
Horn Logic⤓ .md 2026-10-22T093123.000 000000000041216 Alfred Horn, "On sentences which are true of direct unions of algebras" (Journal of Symbolic Logic, 1951) — the clauses are named for a preservation theorem, not for a computational property, and the computational property was found twenty years later. Kowalski (1974) read Horn clauses as procedures; Dowling and Gallier (1984) gave the linear-time propositional algorithm.
Judgment Aggregation⤓ .md 2026-10-22T092834.000 000000000043520 List and Pettit developed judgment aggregation (2002). Extends Arrow's social choice to logic. Aggregate individual judgments on propositions. Impossibility results: no perfect aggregation. Foundation for collective reasoning and deliberation.
Logic Programming⤓ .md 2026-08-20T062802.000 000000000050536 Kowalski's "Predicate logic as a programming language" (1974) proposed the procedural interpretation of Horn clauses: read a clause H :- B₁, ..., Bₙ as a procedure declaration whose body is a list of calls, and resolution becomes execution. Colmerauer and Roussel had built the first Prolog at Marseille in 1972 for natural-language processing, and the two strands converged into a declarative programming paradigm. Van Emden and Kowalski (1976) supplied the fixpoint semantics, Clark (1978) added negation as failure and the program completion, and the language was standardized as ISO/IEC 13211-1 (1995).
Nine-Intersection Model⤓ .md 2026-10-22T180154.561 000000000000904 Max Egenhofer and Robert Franzosa, "Point-set topological spatial relations" (International Journal of Geographical Information Systems 5(2), 1991), defined binary topological relations by the four intersections of two regions' interiors and boundaries; Egenhofer and John Herring, "Categorizing binary topological relations between regions, lines, and points in geographic databases" (technical report, University of Maine, 1991 — circulated from 1990 and cited inconsistently ever since), added the exteriors, giving the 9-intersection. Eliseo Clementini, Paolino Di Felice, and Peter van Oosterom ("A small set of formal topological relationships suitable for end-user interaction", SSD 1993) recorded the dimension of each intersection, and the resulting DE-9IM became the OGC and ISO standard predicate model. Egenhofer and Khaled Al-Taha ("Reasoning about gradual changes of topological relationships", 1992) built the conceptual neighborhood graph; Egenhofer ("Deriving the composition of binary topological relations", Journal of Visual Languages and Computing 5(2), 1994) derived the composition table.
Nonmonotonic Logic⤓ .md 2026-08-20T061445.000 000000000041224 McCarthy introduced circumscription (1980). Reiter developed default logic (1980). McDermott and Doyle on nonmonotonic modal logic (1980). Addresses common-sense reasoning: conclusions may be retracted given more information. Central to AI knowledge representation.
Ontology Languages⤓ .md 2026-10-22T090035.000 000000000048016 The Knowledge Interchange Format (Genesereth and Fikes, 1992) and Ontolingua supplied a first-order interlingua for sharing ontologies but no decidable reasoning. The Semantic Web line began with RDF and RDF Schema, passed through SHOE, OIL and DAML+OIL (2001), and produced OWL as a W3C Recommendation in 2004, deliberately built on description logic so that each species could be given a known complexity bound. OWL 2 followed in 2009, adding qualified cardinality, property chains, keys and a richer datatype map, and introducing three tractable profiles. Common Logic (ISO/IEC 24707, 2007) carries the unrestricted first-order tradition forward alongside.
Paraconsistent Logic⤓ .md 2026-08-20T064854.000 000000000043352 Stanisław Jaśkowski (1948) and Newton da Costa (1963) independently developed logics tolerating contradiction. Motivated by: inconsistent but useful theories (early calculus, naive set theory), real-world databases with conflicts, dialethism (some contradictions are true). Graham Priest developed dialetheism and Logic of Paradox (LP).
Preferential Logic⤓ .md 2026-08-20T061920.000 000000000038664 Kraus, Lehmann, Magidor (1990). KLM framework. Ranked models. Non-monotonic consequence. Foundation of defeasible reasoning.
Region Connection Calculus⤓ .md 2026-10-22T085530.000 000000000059336 Randell, Cui and Cohn (1992) built a spatial logic on a single primitive, connection, following Clarke's (1981) calculus of individuals and behind it Whitehead's proposal that regions rather than points be the basic spatial entities. From C alone the mereological and topological vocabulary is defined, and the eight jointly exhaustive and pairwise disjoint relations that result — RCC-8 — became the standard constraint language of qualitative spatial reasoning. The coarser RCC-5, which drops the tangential distinction, came from the same work.
Rough Set Logic⤓ .md 2026-08-20T074239.000 000000000056520 Pawlak (1982) proposed rough sets as a treatment of a specific kind of incompleteness: not vagueness in a predicate, but limited resolution in the data. Objects are described by finitely many attributes, and objects agreeing on all of them are indiscernible; a set that does not respect this partition cannot be defined exactly, only approximated from within and from without. The theory was developed at the Institute of Computer Science of the Polish Academy of Sciences and grew into a body of work on attribute reduction and rule induction from decision tables.
Situation Calculus⤓ .md 2026-10-22T085254.000 000000000047128 John McCarthy and Patrick Hayes introduced situation calculus (1969) for reasoning about action and change. The frame problem (what doesn't change?) became central. Ray Reiter's solution (1991) using successor state axioms became standard. Foundation for cognitive robotics, planning, and agent programming (Golog).
Tibetan Collected Topics⤓ .md 2026-08-20T082050.000 000000000059864 Tibetan monastic curriculum, systematized 12th-15th c. Cha-ba Chö-kyi Seng-ge, Sakya Pandita, later dGe-lugs codification. Debate training. Collected topics (bsdus grwa) as primer. Foundation of Tibetan Buddhist logic.
Truth Maintenance⤓ .md 2026-10-22T090037.000 000000000038784 Doyle (1979). Track belief dependencies. Reason maintenance under updates. ATMS: assumption-based (de Kleer 1986). JTMS: justification-based. Foundation for belief revision.
Well-Founded Semantics⤓ .md 2026-08-20T084820.000 000000000041160 Van Gelder, Ross, and Schlipf (1988, 1991). A three-valued, uniquely-defined semantics for normal logic programs with negation-as-failure, giving every program a single intended model and standing as the main alternative to the (multiple, two-valued) stable-model/answer-set semantics.
CRITERIA⤓ .txt 2026-10-22T165042.936 000000000000808 Not sufficient: The epistemic modality of knowledge and belief itself (Modal/Epistemic). Degrees of probability (Probabilistic). Rhetorical or dialectical persuasion (Argumentation and Rhetoric).