README⤓ .txt 2026-10-22T165042.936 000000000000792 Formal logics and calculi built to model the meaning of natural language: systems of compositional interpretation, discourse dynamics, quantification, and the pragmatic phenomena that a truth-conditional theory of meaning must handle. The application is linguistic meaning, using logical machinery as the modeling tool.
Alternative Semantics⤓ .md 2026-08-20T014720.000 000000000039928 Hamblin (1973), Rooth (1985). Sets of alternatives. Questions as alternative sets. Focus interpretation. Foundation of question semantics.
Bilateral Logic⤓ .md 2026-08-20T102854.000 000000000033840 Rumfitt (2000), Smiley. Assertion and denial primitive. Two speech acts. Rejection not just negation. Classical logic defended bilaterally.
Categorial Grammar⤓ .md 2026-10-22T090631.000 000000000038320 Ajdukiewicz (1935), Bar-Hillel, Lambek. Categories and slashes. Function-argument structure. Syntax as logic. Foundation of type-logical grammar.
Combinatory Categorial Grammar⤓ .md 2026-10-22T180154.561 000000000000976 Anthony Ades and Mark Steedman, "On the Order of Words" (Linguistics and Philosophy 4, 1982, 517–558), derived unbounded dependencies by composing adjacent categories in a left-to-right processor, replacing movement with partial combination. Anna Szabolcsi (1983) proposed the rule for parasitic gaps that Steedman, "Combinatory Grammars and Parasitic Gaps" (Natural Language and Linguistic Theory 5, 1987, 403–439), identified with Curry's combinator S — every rule the system adds is one of Curry and Feys's combinators. Steedman's The Syntactic Process (MIT Press, 2000) is the full statement; Steedman and Jason Baldridge, "Combinatory Categorial Grammar" (in Borsley and Börjars, eds., Non-Transformational Syntax, Blackwell, 2011, 181–224), is the modern form, with the slash modalities of Baldridge and Kruijff, "Multi-Modal Combinatory Categorial Grammar" (EACL 2003).
Continuation Semantics⤓ .md 2026-08-20T091154.000 000000000052992 Continuations come from denotational semantics of programming languages — Strachey and Wadsworth, "Continuations: a mathematical semantics for handling full jumps" (1974), and Plotkin's CPS transform (1975). Philippe de Groote, "Type raising, continuations, and classical logic" (2001), brought them to Montague semantics; Chris Barker, "Continuations and the nature of quantification" (Natural Language Semantics 10, 2002), argued that quantification just is continuation-taking; Chung-chieh Shan's dissertation Linguistic Side Effects (Harvard, 2005) treated scope, focus, and interrogation as computational effects. Barker and Shan, "Explaining crossover and superiority as left-to-right evaluation" (Linguistics and Philosophy 29, 2006) and Continuations and Natural Language (Oxford, 2014), give the tower calculus.
Degree Semantics⤓ .md 2026-10-22T085910.000 000000000052800 Cresswell, "The semantics of degree" (1976); von Stechow (1984) on comparatives; Kennedy's Projecting the Adjective (1997, published 1999) and his work with McNally (2005); Heim (2000) on degree operators and scope. Gradable adjectives. Degree arguments. Scales and measure functions. Foundation of scalar semantics.
Discourse Representation Theory⤓ .md 2026-10-22T085913.000 000000000054304 Hans Kamp, "A theory of truth and semantic representation" (in Groenendijk, Janssen, and Stokhof, eds., Formal Methods in the Study of Language, 1981), introduced discourse referents and DRS boxes to handle cross-sentential anaphora and donkey sentences, which static Montague semantics cannot bind. Irene Heim's dissertation The Semantics of Definite and Indefinite Noun Phrases (UMass, 1982) reached an equivalent system, File Change Semantics, independently. Kamp and Reyle, From Discourse to Logic (Kluwer, 1993), is the standard reference.
Dynamic Semantics⤓ .md 2026-10-22T085918.000 000000000059072 Irene Heim's File Change Semantics (dissertation, UMass 1982; "On the projection problem for presuppositions", 1983) and Hans Kamp's DRT independently made meaning a context-change operation. Groenendijk and Stokhof, "Dynamic Predicate Logic" (Linguistics and Philosophy 14, 1991), gave the compositional, representation-free version in which formulas denote relations between assignments. Veltman, "Defaults in update semantics" (Journal of Philosophical Logic 25, 1996), extended the idea to epistemic modality with states as sets of possibilities and might as a test. Stalnaker's (1978) common ground is the pragmatic ancestor.
Erotetic Logic⤓ .md 2026-10-22T092948.000 000000000041416 Nuel Belnap and Thomas Steel, The Logic of Questions and Answers (1976), building on Belnap's An Analysis of Questions (1963); Hamblin (1958) and Åqvist's imperative-epistemic reduction (1965) are the other founding lines. Andrzej Wiśniewski's The Posing of Questions (1995) and Questions, Inferences, and Scenarios (2013) give inferential erotetic logic, in which questions stand in consequence relations to each other.
Event Semantics⤓ .md 2026-10-22T085920.000 000000000062112 Donald Davidson, "The Logical Form of Action Sentences" (in Rescher, ed., The Logic of Decision and Action, University of Pittsburgh Press, 1967), argued that action sentences quantify over events, so that adverbial modification is conjunction and adverb-drop inferences become logical rather than lexical. Castañeda, commenting on that paper in the same volume (1967), proposed the neo-Davidsonian variant in which every participant is severed into its own role conjunct. Terence Parsons, Events in the Semantics of English: A Study in Subatomic Semantics (MIT Press, 1990), developed it; Angelika Kratzer, "Severing the External Argument from its Verb" (1996), gave it a syntactic basis. Vendler (1957) and Dowty (1979) supplied the aspectual classes; Bach, "The Algebra of Events" (Linguistics and Philosophy 9, 1986), the mereology.
File Change Semantics⤓ .md 2026-08-20T102911.000 000000000055928 Irene Heim, The Semantics of Definite and Indefinite Noun Phrases (PhD dissertation, University of Massachusetts Amherst, 1982), chapter 3; "File change semantics and the familiarity theory of definiteness" (in Bäuerle, Schwarze, and von Stechow, eds., Meaning, Use, and Interpretation of Language, de Gruyter, 1983); and "On the projection problem for presuppositions" (WCCFL 2, 1983). Hans Kamp's DRT (1981) reached an equivalent system independently. The immediate ancestor is Lewis, "Adverbs of quantification" (1975), from which Heim takes the claim that indefinites are not quantifiers but open formulas bound by whatever operator is around; Stalnaker's common ground is the pragmatic ancestor.
Formal Ethics⤓ .md 2026-08-20T031153.000 000000000050968 Harry J. Gensler, "A formalized ethical theory" in Symbolic Logic: Classical and Advanced Systems (1990), developed fully in Formal Ethics (1996, Routledge). Builds on Castañeda's insistence that deontic operators attach to imperatives, and on Hare's prescriptivism. Gensler is explicit that it is not a complete ethical theory: the theorems are meant to be the largest common subset of the recognized ethical theories, so that no axiom is controversial.
Generalized Quantifiers⤓ .md 2026-10-22T085010.000 000000000045968 Mostowski (1957), Lindström, Barwise & Cooper (1981). Quantifiers as relations. NP denotations. Conservativity. Foundation of quantifier semantics.
Glue Semantics⤓ .md 2026-10-22T090015.000 000000000037568 Mary Dalrymple, John Lamping and Vijay Saraswat, "LFG Semantics via Constraints" (EACL 1993); Fernando Pereira joined the group for "Linear Logic for Meaning Assembly" (1995), which is where the linear-logic formulation is set out in full. LFG interface. Resource-sensitive composition. Foundation of LFG semantics.
Imperative Logic⤓ .md 2026-10-22T092906.000 000000000042224 Jørgen Jørgensen, "Imperatives and logic" (Erkenntnis, 1937–38), which posed the dilemma the field is named for; Alf Ross, "Imperatives and logic" (Theoria, 1941; reprinted 1944), which gave it its standard counterexample; Hare's neustic/phrastic analysis (1952); Segerberg (1990), Hansen (2008), and Vranas (2008, 2011) for the modern treatments.
Inquisitive Logic⤓ .md 2026-08-20T103201.000 000000000038648 Groenendijk, Roelofsen (2000s). Questions in logic. Support semantics. Beyond truth conditions. Foundation for question semantics.
Modern Type Theories Semantics⤓ .md 2026-10-22T184212.000 000000000093128 Göran Sundholm, "Proof theory and meaning" (in Gabbay and Guenthner, eds., Handbook of Philosophical Logic, vol. III, 1986, pp. 471–506), proposed interpreting donkey sentences in Martin-Löf's constructive type theory with Σ-types — Uwe Mönnich's Tübingen Habilitation (1985) made the same proposal — and his "Constructive generalized quantifiers" (Synthese 79(1), 1989, pp. 1–12) extended the treatment to a constructive most. Aarne Ranta, Type-Theoretical Grammar (Oxford UP, 1994), developed natural-language syntax and semantics inside Martin-Löf's intensional type theory, with Σ-types for anaphora; the book laid the program's foundations and posed the multiple-categorisation problem for verbs over many noun types (p. 60). Zhaohui Luo supplied the type theory UTT (Computation and Reasoning: A Type Theory for Computer Science, Oxford UP, 1994), the theory of coercive subtyping ("Coercive subtyping", Journal of Logic and Computation 9(1), 1999, pp. 105–130, after a CSL'96 paper, LNCS 1258), and the program's manifesto, "Formal semantics in modern type theories with coercive subtyping" (Linguistics and Philosophy 35(6), 2012, pp. 491–513). Stergios Chatzikyriakidis and Luo, Formal Semantics in Modern Type Theories (Wiley/ISTE, 2020), is the book-length statement.
Montague Grammar⤓ .md 2026-08-20T010738.000 000000000047456 Richard Montague, "English as a Formal Language" (1970), "Universal Grammar" (1970), and "The Proper Treatment of Quantification in Ordinary English" (PTQ, 1973) — three papers, the last published after his death in 1971. The thesis of the first is that there is no theoretically important difference between natural and formal languages, and that English can be given a model-theoretic semantics by the same means as a logistic system. Barbara Partee brought the programme into linguistics; Dowty, Wall, and Peters, Introduction to Montague Semantics (1981), is the standard textbook; Gallin, Intensional and Higher-Order Modal Logic (1975), gave the metatheory.
Natural Logic⤓ .md 2026-10-22T180154.561 000000000000840 Johan van Benthem, Essays in Logical Semantics (Reidel, 1986) and Language in Action: Categories, Lambdas and Dynamic Logic (North-Holland, 1991), proposed computing entailment on surface forms by marking monotonicity through a categorial parse; Víctor Sánchez Valencia's dissertation Studies on Natural Logic and Categorial Grammar (University of Amsterdam, 1991), written under van Benthem, turned the proposal into the polarity-marking algorithm over Lambek derivations. The dictum de omni et nullo and the terminist conditions of descent and ascent sort term occurrences by the direction of licensed substitution (see Medieval Terminist Logic), Sánchez Valencia's historical chapters trace monotonicity inference through Ockham, Leibniz, De Morgan and Peirce, and Fred Sommers, The Logic of Natural Language (1982), revived term logic with the same ambition of inference on surface form. Icard and Moss, "Recent Progress on Monotonicity" (Linguistic Issues in Language Technology 9, 2014, 167–194), surveys the modern programme.
Plural Semantics⤓ .md 2026-08-20T081641.000 000000000047664 Godehard Link, "The logical analysis of plurals and mass terms: a lattice-theoretical approach" (in Bäuerle, Schwarze, and von Stechow, eds., Meaning, Use, and Interpretation of Language, de Gruyter, 1983), which is the paper the whole field descends from. Sharvy (1980) supplied the maximality analysis of the definite article that Link's σ-operator generalizes; Scha (1981) identified cumulative readings; Landman (1989, "Groups I and II") added group formation; Schwarzschild's Pluralities (Kluwer, 1996) replaced fixed distributivity with contextually supplied covers. Boolos (1984) argued separately that plural quantification needs no plural objects at all.
Possible Worlds Semantics⤓ .md 2026-08-20T082005.000 000000000038128 Carnap's state descriptions and intensions (Meaning and Necessity, 1947); Kripke's model theory for modal logic (1959, 1963); Hintikka's model sets (1961); Montague's intensional logic and "Universal grammar" (1970) and "PTQ" (1973); Lewis, "General semantics" (1970). Intensions as functions. Possible worlds as indices. Foundation of intensional semantics.
Premise Semantics⤓ .md 2026-10-22T165042.936 000000000000872 David Lewis, "Adverbs of quantification" (in Edward Keenan ed., Formal Semantics of Natural Language, Cambridge University Press 1975, 3–15), argued that no plausible semantics for a two-place conditional connective interacts compositionally with always, usually, sometimes to give the right truth conditions, and that if instead marks the restriction of the adverb. Angelika Kratzer generalized the restriction idea to every conditional and built the modal theory it operates in: "What 'must' and 'can' must and can mean" (Linguistics and Philosophy 1, 1977, 337–355), "The notional category of modality" (in Hans-Jürgen Eikmeyer and Hannes Rieser eds., Words, Worlds, and Contexts: New Approaches in Word Semantics, de Gruyter 1981, 38–74), "Partition and revision: the semantics of counterfactuals" (Journal of Philosophical Logic 10, 1981, 201–216), and "Conditionals" (CLS 22, 1986, 1–15). After Irene Heim (1982) applied the analysis to donkey anaphora, Barbara Partee (1991) fixed the name "Lewis/Kratzer/Heim analysis", and it became the dominant treatment of conditionals in linguistics.
Presupposition⤓ .md 2026-10-22T090936.000 000000000036056 Frege (1892) on the presuppositions of definite descriptions; Strawson (1950) against Russell; Karttunen (1973, 1974) on projection and plugs, holes, filters; Stalnaker (1973, 1974) on common ground; Heim's file change semantics (1982, 1983); van der Sandt's anaphoric account (1992). Background entailments. Projection problem. Accommodation. Foundation of pragmatic semantics.
Proof-Theoretic Semantics⤓ .md 2026-10-22T165042.936 000000000000896 Gentzen's remark (1934–35) that the introduction rules "define" the connectives and the eliminations are consequences of that definition. Prawitz turned it into a programme in Natural Deduction (1965) and "Ideas and results in proof theory" (1971); Dummett gave it the philosophical case in The Logical Basis of Metaphysics (1991). The term is Schroeder-Heister's (1991); Francez's Proof-Theoretic Semantics (2015) is the textbook.
Scalar Implicature⤓ .md 2026-08-20T082837.000 000000000050760 Grice, "Logic and conversation" (1975), for the maxim of Quantity and the notion of a conversational implicature; Laurence Horn's dissertation On the Semantic Properties of Logical Operators in English (UCLA, 1972), which introduced the scales; Gazdar (1979) for the first formal implementation; Levinson's Presumptive Meanings (2000) for generalized implicature as a default. The grammatical turn is Chierchia (2004), Fox (2007), and Chierchia, Fox, and Spector (2012), where exhaustification becomes a covert operator in the syntax rather than a pragmatic inference.
Segmented Discourse Representation Theory⤓ .md 2026-10-22T180154.561 000000000001064 Nicholas Asher, Reference to Abstract Objects in Discourse (Kluwer, 1993), extended DRT with rhetorical relations over labelled segments to handle anaphoric reference to propositions and eventualities, which DRT's accessibility both over- and under-generates. Lascarides and Asher, "Temporal Interpretation, Discourse Relations and Commonsense Entailment" (Linguistics and Philosophy 16, 1993, 437–493), supplied the defeasible inference of the relations and their temporal effects. Asher and Lascarides, Logics of Conversation (Cambridge University Press, 2003), is the standard formulation. The glue logic's conditional comes from Asher and Morreau, "Commonsense Entailment: A Modal Theory of Non-monotonic Reasoning" (IJCAI 1991, 387–392); the right frontier constraint is Livia Polanyi's (1985, 1988), proposed for pronouns and generalized by SDRT to all anaphora and all attachment.
Situation Semantics⤓ .md 2026-10-22T180154.561 000000000000888 Jon Barwise and John Perry, Situations and Attitudes (MIT Press, 1983), following Barwise's "Scenes and other situations" (1981). The driving argument was linguistic: naked-infinitive perception reports — "Ralph saw Mary run" — permit substitution of coreferring terms and support existential generalization, yet fail to be closed under logical equivalence, which no possible-worlds semantics can deliver. Keith Devlin, Logic and Information (1991), gave the infon algebra; Barwise and Etchemendy, The Liar (1987), applied the framework to semantic paradox using Aczel's anti-foundation axiom; Barwise and Seligman, Information Flow (1997), developed the constraint machinery into channel theory.
Speech Act Logic⤓ .md 2026-10-22T085209.000 000000000035520 Searle, Vanderveken (1985). Illocutionary logic. Force and content. Speech act theory formalized. Foundation of pragmatic logic.
Tense and Aspect⤓ .md 2026-08-20T084820.000 000000000051640 Reichenbach, Elements of Symbolic Logic (1947), §51, for the three-time analysis; Vendler, "Verbs and times" (Philosophical Review 66, 1957), for the four aspectual classes; Prior's Time and Modality (1957) and Past, Present and Future (1967) for the operator treatment; Kamp's dissertation (UCLA, 1968) for Since and Until; Partee (1973) for the argument that tense is anaphoric; Dowty's Word Meaning and Montague Grammar (1979) for the imperfective paradox; Krifka (1989, 1998) for the mereology of events and incremental themes; Klein's Time in Language (1994) for Topic Time.
Type-Logical Grammar⤓ .md 2026-08-20T061109.000 000000000053312 Michael Moortgat, "Categorial type logics" (Handbook of Logic and Language, 1997), and Glyn Morrill, Type Logical Grammar: Categorial Logic of Signs (1994). The programme takes Lambek's 1958 calculus as a logic rather than a calculus of categories, and asks what happens when the structural rules are made explicit and controlled. Kurtonina and Moortgat, "Structural control" (1997), is the technical centre: the four base systems NL, L, NLP and LP are related by faithful embedding translations that use a unary residuated pair of modalities, so structural options become expressible inside a single fixed logic instead of being fixed by the choice of logic.
Update Semantics⤓ .md 2026-10-22T085316.000 000000000049592 Frank Veltman, "Defaults in update semantics" (Journal of Philosophical Logic 25, 1996), which fixes the system and its slogan; the update conception itself is Stalnaker's (1978) and Heim's (1982), and Veltman's earlier work on data semantics (1985) is the direct ancestor. Groenendijk, Stokhof, and Veltman (1996) combined the epistemic and anaphoric dynamics. Yalcin (2007) and Rothschild and Yalcin (2016, 2017) supply the modern reassessment.
Vector Semantics⤓ .md 2026-08-20T090408.000 000000000049192 Zellig Harris, "Distributional structure" (Word 10, 1954), and Firth, "A synopsis of linguistic theory, 1930–1955" (1957), for the hypothesis; Deerwester, Dumais, Furnas, Landauer, and Harshman (1990) for latent semantic analysis; Church and Hanks (1990) for pointwise mutual information; Turney and Pantel's survey (JAIR 37, 2010) for the vector-space model as a research programme; Mikolov and colleagues (2013) for word2vec and Pennington, Socher, and Manning (2014) for GloVe. The compositional branch is Coecke, Sadrzadeh, and Clark (2010), with Baroni and Zamparelli (2010) for the matrix treatment of adjectives.
CRITERIA⤓ .txt 2026-10-22T182137.000 000000000007920 Not sufficient: A pure model theory absent a linguistic target (Metatheory/Model-Theory). A knowledge-representation formalism (Knowledge). A program semantics (Computation).