
The Boxdot Conjecture and the Generalized McKinsey AxiomAustralasian Journal of Logic 15 (3): 630641. 2018.The Boxdot Conjecture is shown to hold for a novel class of modal systems. Each system in this class is K plus an instance of a natural generalization of the McKinsey axiom. [Note from the editors: This paper was accepted for publication in 2011. It should have been published in 2014. The lateness of the appearance of the article is due entirely to an editorial oversight.]

Topological Models of Belief LogicsDissertation, CUNY Graduate Center. 2007.In this highly original text, Christopher Steinsvold explores an alternative semantics for logics of rational belief. Topologies, as mathematical objects, are typically interpreted in terms of space; here topologies are reinterpreted in terms of an agent with rational beliefs. The topological semantics tells us that the agent can never, in principle, know everything; that the agent's beliefs can never be complete. A number of completeness proofs are given for a variety of logics of rational be…Read more

The Book of Ralph (edited book)Medallion Press. 2016.A message appears on the moon. It is legible from Earth, and almost no one knows how it was created. Markus West leads the government’s investigation to find the creator. The message is simple and familiar. But those three words, written in blazing crimson letters on the lunar surface, will foster the strangest revolution humankind has ever endured and make Markus West wish he was never involved. The message is ‘Drink Diet Coke.’ When CocaCola denies responsibility, global annoyance becomes ind…Read more

A canonical topological model for extensions of K4Studia Logica 94 (3). 2010.Interpreting the diamond of modal logic as the derivative, we present a topological canonical model for extensions of K4 and show completeness for various logics. We also show that if a logic is topologically canonical, then it is relationally canonical.

Being Wrong: Logics for False BeliefNotre Dame Journal of Formal Logic 52 (3): 245253. 2011.We introduce an operator to represent the simple notion of being wrong. Read Wp to mean: the agent is wrong about p . Being wrong about p means believing p though p is false. We add this operator to the language of propositional logic and study it. We introduce a canonical model for logics of being wrong, show completeness for the minimal logic of being wrong and various other systems. En route we examine the expressiveness of the language. In conclusion, we discuss an open question regarding K4

A Grim Semantics For Logics of BeliefJournal of Philosophical Logic 37 (1): 4556. 2008.Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics, and we suggest that the condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for K4 and KD4.

Completeness for various logics of essence and accidentBulletin of the Section of Logic 37 (2): 93102. 2008.

The Boxdot Conjecture and the Language of Essence and AccidentAustralasian Journal of Logic 10 1835. 2011.We show the Boxdot Conjecture holds for a limited but familiar range of LemmonScott axioms. We reintroduce the language of essence and accident, first introduced by J. Marcos, and show how it aids our strategy

A Note on Logics of Ignorance and BordersNotre Dame Journal of Formal Logic 49 (4): 385392. 2008.We present and show topological completeness for LB, the logic of the topological border. LB is also a logic of epistemic ignorance. Also, we present and show completeness for LUT, the logic of unknown truths. A simple topological completeness proof for S4 is also presented using a T1 space
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