In this introduction to the Outstanding contributions to logic volumedevoted to Nuel Belnap’s work on indeterminism and free action, we provide abrief overview of some of the formal frameworks and methods involved in Belnap’swork on these topics: theories of branching histories, specifically “branchingtime” and “branching space-times”, the stit (“seeing to it that”) logic of agency, andcase-intensional first order logic. We also draw some connections to the contributionsincluded in this volume. Abstracts of these contributions are included as anappendix.Nuel Belnap’s work in logic and in philosophy spans a period of over half a century.During this time, he has followed a number of different research lines, most of themover a period of many years or decades, and often in close collaboration with otherresearchers:1 relevance logic, a long term project starting from a collaboration withAlan Anderson dating back to the late 1950s and continued with Robert Meyerand Michael Dunn into the 1990s; the logic of questions, developed with ThomasSteel in the 1960s and 1970s; display logic in the 1980s and 1990s; the revisiontheory of truth, with Anil Gupta, in the 1990s; and a long-term, continuing interestin indeterminism and free action. This book is devoted to Belnap’s work on the lattertwo topics. In this introduction, we provide a brief overview of some of the formalframeworks and methods involved in thatwork, and we drawsome connections to thecontributions included in this volume. Abstracts of these contributions are presentedin Appendix A.

- Contents
- 1 Introduction: The Many Branches of Belnap's Logic
- 1 About this Book
- 2 State of the Art: BT, BST, stit, and CIFOL
- 2.1 Branching Time (BT)
- 2.2 Branching Space-Times (BST)
- 2.3 Seeing to it That (stit)
- 2.4 Case-Intensional First Order Logic (CIFOL)

- References

- 2 Decisions in Branching Time
- 1 Introduction: Decision Theory and Deontic Logic
- 2 Seeing to it That (stit)
- 2.1 Semantics for cstit with One Agent
- 2.2 Multiple Agents: Independence and Joint Agency

- 3 Causal Independence
- 4 Horty's Dominance Ought
- 5 Decisions Under Ignorance: The Maximin Ought
- 6 Decision Under Risk: Probabilistic Utilitarian stit Frames
- 7 Game Theory and Mixed Strategies
- 8 Conclusion
- References

- 3 Internalizing Case-Relative Truth in CIFOL+
- 1 Introduction
- 1.1 Grammar and Semantics
- 1.2 Finding ``True in a Case'' in CIFOL+
- 1.3 Paths not Taken
- 1.4 Extending CIFOL
- 1.5 Picturing Intensions

- 2 Theory of Internal Ranges
- 2.1 CIFOL+ and Elementary Ranges

- 3 Proving Theorem 1
- 4 The concept of case-relative truth
- 5 Summary
- References

- 1 Introduction
- 4 A stit Logic Analysis of Morally Lucky and Legally Lucky Action Outcomes
- 1 Introduction
- 2 Modeling Indeterminacy of Action
- 2.1 Determinate Action: XSTITp
- 2.2 Action with Non-Determinate Effect: XSTIT.Prob

- 3 Modeling the Determination in Action
- 3.1 Risk in Action
- 3.2 Attempt

- 4 Moral Obligations, Prohibitions and Luck
- 5 Legal Obligations, Prohibitions and Luck
- 6 Discussion
- 7 Conclusion
- References

- 5 Worlds Enough, and Time: Musings on Foundations
- 1 Core Features of Ockhamist Branching Time
- 2 Newton Versus Einstein
- 3 The Enigmatic Present
- 4 What is a World?
- 5 Chronological Unity and Belnap's World(s)
- 6 The General Character of Models
- 7 Comparing Belnapian Worlds
- 8 Belnapian Multi-Worlds
- 9 The Making of an Agent
- 10 Conclusion
- Bibliography

- 6 Open Futures in the Foundations of Propositional Logic
- 1 Introduction
- 2 What Rules Express
- 3 What Intuitionistic Logic Expresses
- 4 Open Future Semantics
- 5 What Propositional Logic Expresses
- 6 What Natural Deduction Rules for Disjunction Express
- 7 No Past Branching
- 8 Open Future Semantics and Supervaluations
- 9 Defeating Fatalism
- References

- 7 On Saying What Will Be
- 1 Branching Time and Ontic Frugality
- 2 Some Concepts from Speech Act Theory
- 2.1 Speech Acts Versus Acts of Speech
- 2.2 Saying Versus Asserting
- 2.3 Two Levels of Determination
- 2.4 Assertion Proper and the Assertive Family

- 3 Assertion and Scorekeeping
- 4 Future-Directed Speech Acts
- 5 The Assertion Problem
- 6 The Modal Realism Objection
- References

- 8 The Intelligibility Question for Free Will: Agency, Choice and Branching Time
- 1 The Intelligibility Question: An Introductory Narrative
- 2 Action, Indeterminism, and Facing the Future
- 3 From Action to Free Will
- 4 Self-forming Actions (SFA's)
- 5 Further Issues: Efforts, Introspection, Agency, Control, Rationality
- References

- 9 What William of Ockham and Luis de Molina Would have said to Nuel Belnap: A Discussion of Some Arguments Against ``The Thin Red Line''
- 1 There is No Truth Concerning Future Contingents
- 2 A Thin Red Line Theory is Insufficient as a Background for a Proper Understanding of the Structure of Tenses in Natural Language
- 3 An Obvious Requirement Regarding Iterative Tenses Makes TRL Theories Problematic
- 4 TRL Theories Lead to Problematic Evaluations at Counterfactual Moments of Time
- References

- 10 Branching for General Relativists
- 1 Introduction
- 2 BST with a New PCP
- 3 How to Generalize BST1992?
- 4 Construction
- 4.1 BST Generalized
- 4.2 Generalized Differential Manifolds and Matters Topological
- 4.3 Tangent Vectors

- 5 Discussion
- 5.1 Hájíček-Müller Quasi-History
- 5.2 Borders in the Overlap

- 6 Conclusions
- References

- 11 Some Examples Formulated in a `Seeing to It That' Logic: Illustrations, Observations, Problems
- 1 Introduction
- 2 Syntax and Semantics
- 2.1 Preliminaries: Transition Systems
- 2.2 Agency Modalities
- 2.3 Acts Differently
- 2.4 `Brings It About' Modalities

- 3 Example: Vase (One Agent)
- 4 Example: Vase (Two Agents)
- 5 Example: Vase, Minor Variation
- 6 Example: Table
- 7 Example: Avoidance (Fixed)
- 8 Example: Avoidance (Reaction)
- 9 Example: Granularity
- 10 Conclusion
- References

- 12 In Retrospect: Can BST Models be Reinterpreted for What Decisions, Speciation Events and Ontogeny Might Have in Common?
- 1 Introduction
- 2 First Step: BST Structures and Structures of FTA
- 2.1 BST Structures
- 2.2 BTA Structures
- 2.3 BTA+U Structures are BST Structures
- 2.4 What Does it all Mean?
- 2.5 The Unity of Life
- 2.6 What Else Can be Done with BTA?

- 3 Retrospect
- 3.1 The Story so Far
- 3.2 Theory of Possible Ancestry (TPA)
- 3.3 The Growth of Life Itself
- 3.4 Speciation
- 3.5 Individual Ontogeny

- 4 Afterthought: Resuscitation and Decisions
- 5 Summary
- References

- 13 A Theory of Possible Ancestry in the Style of Nuel Belnap's Branching Space-Time
- 1 Ersatzism of Belnapian Elegance
- 2 The Basic Theory of Possible Ancestry
- 3 The General Form of a Theory of Possible Ancestry and Some Specific Theories
- 4 The Question of Embeddability: States, Moments, and Histories
- 5 Ontological Competition
- 6 Back To Branching Space-Time: General Relativity
- References

- 14 Connecting Logics of Choice and Change
- 1 Introduction: Logical Frameworks for Agency
- 2 Preliminaries: The STIT Framework
- 3 Modeling Choice Situations
- 3.1 The Modal Heart of Choice
- 3.2 An Initial Comparison with Modal Logics of Action
- 3.3 Merging the Two Perspectives on Action

- 4 A Merged System: Matrix Game Logic
- 4.1 Modal logic of matrix games
- 4.2 STIT in Modal Matrix Logic
- 4.3 Complexity and Correlation

- 5 The Roles of Knowledge
- 6 Dynamic Epistemic Logic Meets STIT
- 7 Further Directions
- 8 Conclusion
- References

- 15 Intentionality and Minimal Rationality in the Logic of Action
- 1 Analysis of Propositional Contents of Attitudes
- 2 My New Approach in the Logic of Propositional Attitudes
- 2.1 Analysis of Psychological Modes and Possession Conditions of Attitudes
- 2.2 Analysis of Satisfaction Conditions of Propositional Attitudes

- 3 Intentionality in the Logic of Action
- 4 Fundamental Valid Laws
- References

- 16 Group Strategies and Independence
- 1 Stit Frames
- 2 Outcomes
- 3 Fields and Outcomes Bordering Fields
- 4 Strategies and Their Admitted Future Outcomes
- 5 Pre-Simple Strategies and Complete Strategies
- 6 Group-Joining Meets
- 7 Distinguishability
- 8 Inactivity and Busyness
- 9 Independence
- References

- 17 Biographical Interview
- 1 School Days
- 2 From BA at Illinois to Grad School at Yale
- 3 From Yale to Pittsburgh
- 4 Employment History at Pitt
- 5 Visiting Professorships
- 6 Professional Service
- 7 Journals
- 8 Prizes and Fellowships
- 9 Honors
- 10 Doctoral Students
- 11 Publications

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