Possibility Semantics is a generalization of Possible World Semantics, based on partial possibilities instead of complete possible worlds. In recent years, this approach has been applied to the semantics of modal and non-classical logics, natural language semantics, and semi-constructive mathematics. In this course, we will provide: a more accessible introduction to Possibility Semantics than is available in the technical literature (Day 1); in-depth sample applications of Possibility Semantics to the formal semantics of epistemic modals in natural language (Days 2-3), the modeling of knowledge and awareness (Day 4), temporal logic and the openness of the future (Day 5), and an introduction to propositional and first-order quantification in possibility semantics (Day 5, time permitting). No previous familiarity with Possibility Semantics will be assumed. Over the course of the week, we will suggest a number of open problems and avenues for future research.
Day 1: What Is Possibility Semantics?
Slides: here
Associated reading:
1.1 Classical possibility semantics
Sections 1-3.32 of "Possibility Semantics"
1.2 Non-classical possibility semantics
Sections 1-2 of "Compatibility and accessibility"
Section 4 of "A Fundamental Non-Classical Logic"
1.3 Adding modality
"From Worlds to Possibilities"
Section 5.3.1 of "Possibility Semantics"
Section 4 of "Compatibility and accessibility"
Day 2-3: Epistemic modals
Slides: here
Associated reading: Sections 1-5 of "The Orthologic of Epistemic Modals"
Day 4: Knowledge and awareness
Slides: here
Associated reading: "A partial-state space model of unawareness"
Day 5, Part I: Time
Slides: here
Associated reading:
Examples 5.3.9 and 5.3.10 and Section 6.1 of "Possibility Semantics"
"Modeling future indeterminacy in possibility semantics"
Day 5, Part II (time permitting): Quantification
Slides: here
Associated reading:
5.1 Propositional quantification
Section 5.1 of "Possibility Semantics"
5.2 First-order quantification
Sections 4 and 5.5 of "Possibility Semantics"
Bazzoni (2017), "Philosophical foundations of partial belief models."
van Benthem (2016), "Tales from an old manuscript."
van Benthem, Bezhanishvili, and Holliday (2017), "A bimodal perspective on possibility semantics."
van Benthem (2021), "Relational Patterns, Partiality, and Set Lifting in Modal Semantics."
G. Bezhanishvili and Holliday (2019), "A semantic hierarchy for intuitionistic logic."
N. Bezhanishvili and Holliday (2020), "Choice-free Stone duality."
Bonnay and Westerstahl (2016), "Compositionality solves Carnap's problem."
Cariani (2022), "Modeling future indeterminacy in possibility semantics."
Ding and Holliday (2020), "Another problem in possible world semantics."
Fine (2018), "The World of Truth-Making."
Flocke (2021), "How to engineer a concept."
Garson (2013), What Logics Mean: From Proof Theory to Model-Theoretic Semantics.
Harrison-Trainor (2017), "A representation theorem for possibility models."
Harrison-Trainor (2019), "First-order possibility models and finitary completeness proofs."
Holliday (2014), "Partiality and Adjointness in Modal Logic."
Holliday (2015), "Possibility Frames and Forcing for Modal Logic."
Holliday (2021), "Possibility Semantics."
Holliday (2022), "Compatibility and accessibility: lattice representations for semantics of non-classical and modal logic."
Holliday (2023), "A Fundamental Non-Classical Logic."
Holliday and Mandelkern (2021), "The Orthologic of Epistemic Modals."
Humberstone (1981), "From Worlds to Possibilities."
Humberstone (2019), "Supervenience, Dependence, Disjunction."
Massas (2016), "Possibility spaces, Q-completions and Rasiowa-Sikorski lemmas for non-classical logics."
Massas (2021), "A semi-constructive approach to the hyperreal line."
Yalcin (2016), "Belief as question-sensitive."
Yamamoto (2017), "Results in modal correspondence theory for possibility semantics."
Zhao (2021), "Algorithmic correspondence and canonicity for possibility semantics."