Groupings: (I) singly authored pieces, (II) co-authored pieces (excluding reviews etc.), (III) books, (IV) critical notices and book reviews, and (V) published abstracts of papers delivered to conferences. Some of these publications have ‘Lloyd Humberstone’ as the name of the author while others have ‘I. L. Humberstone’. The entries are in reverse chronological order (latest first, that is). See also (VI) for some unpublished material.

I. Singly Authored Articles and Discussion Notes

‘Note on Extending Congruential Modal Logics’, Notre Dame Journal of Formal Logic 57 (2016), 95–103.

‘Béziau on And and Or‘, pp. 283–307 in Arnold Koslow and Arthur Buchsbaum (eds.), The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, Volume I, Springer-Birkhäuser 2015.

‘Prior’s OIC Nonconservativity Example Revisited’, Journal of Applied Non-Classical Logics 24 (2014), 209–235.

‘Power Matrices and Dunn–Belnap Semantics: Reflections on a Remark of Graham Priest’, Australasian Journal of Logic 11 (2014), 14–45.

‘Logical Relations’, Philosophical Perspectives 27 (2013), 176–230.

‘Aggregation and Idempotence’, Review of Symbolic Logic 6 (2013), 680–708.

‘Zolin and Pizzi: Defining Necessity from Noncontingency’, Erkenntnis 78 (2013), 1275–1302.

‘Inverse Images of Box Formulas in Modal Logic’, Studia Logica 101 (2013), 1031–1060.

‘Replacement in Logic’, Journal of Philosophical Logic 42 (2013), 49–89.

“Minimally Congruential Contexts: Observations and Questions on Embedding E in K“, Notre Dame Journal of Formal Logic 53 (2012), 581–598.

“Dana Scott’s Work with Generalized Consequence Relations”, pp. 263–279 in J.-Y. Béziau (ed.), Universal Logic: an Anthology, Birkhäuser (Springer), Basel 2012.

“On a Conservative Extension Argument of Dana Scott”, Logic Journal of the IGPL 19 (2011), 241–288.

“Variation on a Trivialist Argument of Paul Kabay”, Journal of Logic, Language and Information 20 (2011), 115–132.

“Sentence Connectives in Formal Logic”, The Stanford Encyclopedia of Philosophy, (Summer 2010 Edition), Edward N. Zalta (ed.).

“Smiley’s Distinction Between Rules of Inference and Rules of Proof”, pp. 107–126 in J. Lear and A. Oliver (eds.), The Force of Argument: Essays in Honor of Timothy Smiley, Routledge, NY 2010.

“Collapsing Modalities”, Note Dame Journal of Formal Logic 50 (2009), 119–132.

“Can Every Modifier be Treated as a Sentence Modifier?”, Philosophical Perspectives 22 (2008), 241–275.

“Replacing Modus Ponens With One-Premiss Rules”, Logic Journal of the IGPL 16 (2008), 431–451.

“Modal Formulas True at Some Point in Every Model”, Australasian Journal of Logic 6 (2008), 70–82. (

“Investigations into a Left-Structural Right-Substructural Sequent Calculus”, Journal of Logic, Language and Information16 (2007), 141–171.

“Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness”, Journal of Philosophical Logic 36(2007), 1–32.

“Sufficiency and Excess”, Aristotelian Society Supplementary Volume 80 (2006), 265–320.

“Variations on a Theme of Curry”, Notre Dame Journal of Formal Logic 47 (2006), 101–131.

“Extensions of Intuitionistic Logic Without the Deduction Theorem”, Reports on Mathematical Logic 40 (2006), 45–82.

“Weaker-to-Stronger Translational Embeddings in Modal Logic”, pp. 279-297 in G. Governatori, I. Hodkinson, and Y. Venema (eds.), Advances in Modal Logic, Vol. 6, College Publications, London 2006.

“Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCSK Fragment of S5”, Journal of Philosophical Logic 35 (2006), 435–487; erratum, ibid. 36 (2007), 249.

“Modality”, pp. 534–614 ( = Chapter 20) in F. C. Jackson and M. Smith (eds.), The Oxford Handbook of Contemporary Philosophy, Oxford University Press, Oxford and New York 2005.

“Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.-Y. Béziau)”,Theoria 71 (2005), 241–262.

“Béziau”s Translation Paradox”, Theoria 71 (2005), 138–181.

“For Want of an ‘And’: A Puzzle About Non-Conservative Extension”, History and Philosophy of Logic 26 (2005), 229–266.

“Geach’s Categorial Grammar”, Linguistics and Philosophy 28 (2005), 281–317.

“Logical Discrimination”, pp.207–228 in J.-Y. Béziau (ed.), Logica Universalis: Towards a General Theory of Logic, Birkhäuser, Basel 2005.

“Yet Another ‘Choice-of-Primitives’ Warning: Normal Modal Logics”, Logique et Analyse 47 (2004), 395–407.

“Archetypal Forms of Inference”, Synthese 141 (2004), 45–76.

“Two-Dimensional Adventures”, Philosophical Studies 118 (2004), 17–65.

“On a Strange Remark Attributed to Gödel”, History and Philosophy of Logic 24 (2003), 39–44.

“False Though Partly True – An Experiment in Logic”, Journal of Philosophical Logic 32 (2003), 613–665.

“Note on Contraries and Subcontraries”, Noûs 37 (2003), 690–705.

“Invitation to Autoepistemology”, Theoria 68 (2002), 13–51.

“The modal logic of agreement and noncontingency”, Notre Dame Journal of Formal Logic 43 (2002), 95–127.

“Implicational Converses”, Logique et Analyse 45 (2002), 61–79.

“Note on a Lemma of Komori”, Scientiae Mathematicae Japonicae 53 (2001), 347–352.

“The Pleasures of Anticipation: Enriching Intuitionistic Logic”, Journal of Philosophical Logic 30 (2001), 395–438.

“What Fa Says About a, Dialectica 54 (2000), 1–28.

“The Revival of Rejective Negation”, Journal of Philosophical Logic 29 (2000), 331–381.

“Contra-Classical Logics”, Australasian Journal of Philosophy 78 (2000), 438–474.

“Parts and Partitions”, Theoria 66 (2000), 41–82.

“An Intriguing Logic with Two Implicational Connectives”, Notre Dame Journal of Formal Logic 41 (2000), 1–41.

“Equivalential Interpolation”, pp. 36–53 in The Goldblatt Variations: Eight Papers in Honour of Rob, an informal Festschrift for Rob Goldblatt, edited (anonymously) by Krister Segerberg, Uppsala Prints and Preprints in Philosophy, Uppsala University 1999.

“Many-Valued Logics, Philosophical Issues in”, pp. 84–91 in Vol. 6 of E. Craig (ed.) Routledge Encyclopedia of Philosophy, Routledge, London 1998.

“‘Yes, I Agree'”, Studies in Language 22 (1998), 619–659.

“Note on Supervenience and Definability”, Notre Dame Journal of Formal Logic 39 (1998), 243–252.

“Choice of Primitives: A Note on Axiomatizing Intuitionistic Logic”, History and Philosophy of Logic 19 (1998) 31–40.

“Singulary Extensional Connectives: A Closer Look”, Journal of Philosophical Logic 26 (1997), 341–356.

“Two Types of Circularity”, Philosophy and Phenomenological Research 58 (1997), 249–281.

“A Study in Philosophical Taxonomy”, Philosophical Studies 83 (1996), 121–169.

“Classes of Valuations Closed Under Operations Galois-Dual to Boolean Sentence Connectives”, Publicns. of the Research Institute for Mathematical Sciences, Kyoto University 32 (1996), 9–84.

“Valuational Semantics of Rule Derivability”, Journal of Philosophical Logic 25 (1996), 451–461.

“Intrinsic/Extrinsic”, Synthese 108 (1996), 205–267.

“Homophony, Validity, Modality”, pp.215–236 in B. J. Copeland (ed.), Logic and Reality: Essays on the Legacy of A. N. Prior, Clarendon Press, Oxford 1996.

“A Basic System of Congruential-to-Monotone Bimodal Logic and Two of its Extensions”, Notre Dame Journal of Formal Logic 37 (1996), 602–612.

“Comparatives and the Reducibility of Relations”, Pacific Philosophical Quarterly 76 (1995), 117–141.

“The Logic of Non-Contingency”, Notre Dame Journal of Formal Logic 36 (1995), 214–229.

“Names and Pseudonyms”, Philosophy 70 (1995), 487–512.

“Negation by Iteration”, Theoria 61 (1995), 1–24.

“Hempel Meets Wason”, Erkenntnis 41 (1994), 391–402.

“Zero-place Operations and Functional Completeness (and the Definition of New Connectives)”, History and Philosophy of Logic 14 (1993), 39–66.

“Functional Dependencies, Supervenience, and Consequence Relations”, Journal of Logic, Language and Information 2 (1993), 309–336.

“Direction of Fit”, Mind 101 (1992), 59–83.

“Some Structural and Logical Aspects of the Notion of Supervenience”, Logique et Analyse 35 (1992), 101–137.

“Two Kinds of Agent-Relativity”, Philosophical Quarterly 41 (1991), 144–166.

“A Study of Some ‘Separated’ Conditions on Binary Relations”, Theoria 57 (1991), 1–16.

“Wanting, Getting, Having”, Philosophical Papers 19 (1990), 99–118.

“Expressive Power and Semantic Completeness: Boolean Connectives in Modal Logic”, Studia Logica 49 (1990), 197–214.

“Operational Semantics for Positive R “, Notre Dame Journal of Formal Logic 29 (1988), 61–80.

“Heterogeneous Logic”, Erkenntnis 29 (1988), 395–435.

“Some Epistemic Capacities”, Dialectica 42 (1988), 183–200.

“Wanting as Believing”, Canadian Journal of Philosophy 17 (1987), 49–62.

“The Modal Logic of ‘All and Only'”, Notre Dame Journal of Formal Logic 28 (1987), 177–188.

“Extensionality in Sentence Position”, Journal of Philosophical Logic 15 (1986), 27–54. (Corrigendum: “The Lattice of Extensional Connectives: A Correction”, Journal of Philosophical Logic 17 (1988), 221–223.)

“The Formalities of Collective Omniscience”, Philosophical Studies 48 (1985), 410–423.

“Monadic Representability of Certain Binary Relations”, Bulletin of the Australian Mathematical Society 29 (1984), 365–375.

“The Background of Circumstances”, Pacific Philosophical Quarterly 64 (1983), 19–34.

“Inaccessible Worlds”, Notre Dame Journal of Formal Logic 24 (1983), 346–352.

“Karmo on Contingent Non-identity”, Australasian Journal of Philosophy 61 (1983), 188–191.

“First Steps in Philosophical Taxonomy”, Canadian Journal of Philosophy 12 (1982), 467–478.

“Scope and Subjunctivity”, Philosophia 12 (1982), 99–126.

“Necessary Conclusions”, Philosophical Studies 41(1982), 321–335.

“From Worlds to Possibilities”, Journal of Philosophical Logic 10 (1981), 313–339.

“Relative Necessity Revisited”, Reports on Mathematical Logic 13 (1981), 33–42.

“A Note on Two Remarks of Wiggins concerning Restricted Quantification”, Australasian Journal of Philosophy 59 (1981), 432–437.

“You’ll Regret It”, Analysis 40 (1980), 175–176.

“Interval Semantics for Tense Logic: Some Remarks”, Journal of Philosophical Logic 8 (1979), 171–196.

“Two Merits of the Circumstantial Operator Language for Conditional Logics”, Australasian Journal of Philosophy 56 (1978), 21–24.

“Logic for Saints and Heroes”, Ratio 16 (1974), 103–114.

“Two Sorts of ‘Ought’s”, Analysis 32 (1971), 8–11.

II. Jointly Authored Articles and Discussion Notes

Note: a subscripted ‘1’ on the word ‘with’ means that I am the first-named author, a ‘2’ that I am the second-named. The same convention is used for co-authored entries in Sections III (Critical Notices and Reviews).

(with2 Tomasz Kowalski) ‘An Abelian Rule for BCI – and Variations’, Notre Dame Journal of Formal Logic 57 (2016), 551–568.

(with2 Rohan French) ‘An Observation Concerning Porte’s Rule in Modal Logic’ Bulletin of the Section of Logic 44 (2015), 25–31.

(with1 David Makinson) “Intuitionistic Logic and Elementary Rules”, to appear in Mind 120 (2011), 1035–1051.

(with2 Rohan French) “Partial Confirmation of a Conjecture on the Boxdot Translation in Modal Logic”, Australasian Journal of Logic 7 (2009), 56–61.

(with1 Robert K. Meyer), “The Relevant Equivalence Property”, Logic Journal of the IGPL 15 (2007), 165–181.

(with2 A. P. Hazen) “Similarity Relations and the Preservation of Solidity” Journal of Logic, Language and Information13 (2004), 25–46.

(with1 Timothy Williamson) “Inverses for Normal Modal Operators”, Studia Logica 59 (1997), 33–64.

(with1 A. V. Townsend) “Co-instantiation and Identity”,Philosophical Studies 74 (1994), 243–272.

(with2 S. R. Blamey) “A Perspective on Modal Sequent Logic”,Publicns. of the Research Institute for Mathematical Sciences, Kyoto University, 27 (1991), 763–782.

(with2 J. A. Burgess) “Natural Deduction Rules for a Logic of Vagueness”, Erkenntnis 27 (1987), 197–229.

(with1 A. J. Lock) “Semicomplemented Lattices and the Finite Model Property”, Zeitschrift fur math. Logik und Grundlagen der Math. 32 (1986), 431–437.

(with2 J. F. A. K. van Benthem) “Halldén-completeness by Gluing of Kripke Frames”, Notre Dame Journal of Formal Logic 24 (1983), 426–430.

(with2 F. C. Jackson) “On a Challenge by Anderson and Belnap”, Analysis 42 (1982), 179–181.

(with2 M. K. Davies) “Two Notions of Necessity”, Philosophical Studies 38 (1980), 1–30.

(with2 J. N. Crossley) “The Logic of ‘Actually'”, Reports on Mathematical Logic 8 (1977), 11–29.

(with1 J. M. Bell) “Two Systems of Presupposition Logic”, Notre Dame Journal of Formal Logic 18 (1977), 321–339.

III. Book(s)

Philosophical Applications of Modal Logic, College Publications, London 2016.

The Connectives, MIT Press, Cambridge, Mass. 2011.

IV. Critical Notices and Book Reviews

Review of Alex Oliver and Timothy Smiley, Plural Logic (Oxford University Press, 2013), Australasian Journal of Philosophy 93 (2015), 192–195.

Review of John P. Burgess, Philosophical Logic (Princeton University Press, 2009), Bulletin of Symbolic Logic 16 (2010), 411–413.

Review of J. C. Beall and Greg Restall, Logical Pluralism (Oxford University Press, 2006), Australasian Journal of Philosophy 87 (2009), 162–168.

Review of Maarten Marx and Yde Venema, Multi-Dimensional Modal Logic (Kluwer, Dordrecht 1997), Studia Logica 65 (2000), 278–282.

Review of Heinrich Wansing (ed.), Negation: A Notion in Focus (de Gruyter, Berlin 1996), Studia Logica 63 (1999), 293–296.

Review of J. P. Cleave, A Study of Logics (Oxford: Clarendon Press 1991) and A. Koslow, A Structuralist Theory of Logics (Cambridge: Cambridge University Press 1992), Australasian Journal of Philosophy73 (1995), 475–481.

Review of K. Devlin, Logic and Information (Cambridge University Press 1991), Journal of Symbolic Logic 58 (1993), 1082–1084.

Reviews of J. M. Dunn and A. Gupta (eds.) Truth or Consequences(Kluwer: 1990), G. Priest, R. Routley, and J. Norman (eds.), Paraconsistent Logic (Philosophia Verlag: 1989), and H. A. Lewis (ed.), Peter Geach: Philosophical Encounters (Kluwer 1991), Australasian Journal of Philosophy 70 (1992), 362–369.

Review of G. Forbes, Languages of Possibility (Clarendon Press, Oxford: 1989), Journal of Symbolic Logic 56 (1991), 351–352.

Reviews of D. H. Sanford, If P then Q (Routledge: 1989) and S. Read,Relevant Logic (Blackwell: 1989), Australasian Journal of Philosophy 69 (1991), 233–236.

Critical Notice of F. C. Jackson, Conditionals (Blackwell: 1987), Philosophy and Phenomenological Research 51 (1991), 227–234.

Review of R. A. Sorensen, Blindspots (Clarendon Press, Oxford: 1988), Australasian Journal of Philosophy 68 (1990), 119–121.

Review of M. Luntley, Language, Logic, and Experience (Duckworth: 1988), Australasian Journal of Philosophy 68 (1990), 465–467.

Review of C. L. Hamblin, Imperatives (Blackwell: 1986),Australasian Journal of Philosophy 67 (1989), 239–241.

Critical Notice of J. Hintikka and J. Kulas, The Game of Language(Reidel: 1983), Mind 96 (1987), 99–107.

Reviews of D. Gabbay and F. Guenthner (eds.) Handbook of Philosophical Logic (Reidel: 1983–1986), Vol. 1 reviewed in Australasian Journal of Philosophy 63 (1985), 369–372; Vol. 2 reviewed ibid. 64 (1986), 109–114; Vol. 3 reviewed ibid. 66 (1988), 120–126; Vol. 4 reviewed ibid. 70 (1992), 366–369.

Review of H.-J. Eikmeyer and H. Rieser (eds.) Words, Worlds, and Contexts: New Approaches in Word Semantics (de Gruyter: 1981),Australasian Journal of Philosophy 62 (1984), 197–199.

Review of N. Denyer, Time, Action, and Necessity: A Proof of Free Will (Duckworth: 1981), Mind 92 (1983), 461–464.

Review of M. Platts (ed.) Reference, Truth, and Reality (Routledge: 1980), Australasian Journal of Philosophy 59 (1981), 464–470.

Critical Notice of E. L. Keenan (ed.), Formal Semantics of Natural Language (Cambridge: 1975), Australasian Journal of Philosophy 57 (1979), 171–182.

Review of D. Davidson and G. Harman (eds.), Semantics of Natural Language (Reidel, Dordrecht: 1972), York Papers in Linguistics 5 (1975), 195–224.

Critical Notice of M. Kroy, The Conscience (John Wiley: 1974), Noûs 13 (1979), 397–402.

“Science, Theory, and Dogma” (with2 Geoffrey K. Pullum), Review Article of Robert A. Hall, Jr., An Essay on Language,York Papers in Linguistics 1 (1971), 123–131.

V. Published Abstracts

“A Conservative Extension Argument of Dana Scott”, Bulletin of Symbolic Logic 16 (2010), 447–448.

“A Left-Structural Right-Substructural Sequent Calculus for Fission”, Bulletin of Symbolic Logic 10 (2004), 292.

“Béziau”s Paradox”, Bulletin of Symbolic Logic 9 (2003), 257.

“An Intriguing Logic with Two Implicational Connectives”, Bulletin of Symbolic Logic 6 (2000), 251.

“What Fa Says About a“, Bulletin of Symbolic Logic 3 (1997), 365.

“A More Discriminating Approach to Modal Logic”, Journal of Symbolic Logic 51 (1986), 503–504.

“Unique Characterization of Connectives”, Journal of Symbolic Logic 49 (1984), 1426–1427.

“An Alternative Account of Bringing About”, Bulletin of the Section of Logic (Polish Academy of Sciences) 6 (1977), 144–145; reprinted in The Relevance Logic Newsletter 2 (1977), 107–108.

VI. Unpublished Material

“Propositional Attitudes: Some Logical Issues” (Selected Papers 1982–1997).

“How Not to Think About Modal Definability: A Modal Axiom From G. E. Hughes”.

“The Consequence Relation of Tautological Entailment is Maximally Relevant: Answering a Question of Graham Priest”.