-My research consists in the foundations, and philosophy of probability, and developing a novel conception of single case objective chance.

This concerns the nature of single case objective chance (propensity) and its relation to logic and full belief, credence, and counter-factual/conditional logic, and decision theory vis a vis qualitative dominance/logic -state-wise-dominance/conditional-logic dominance.

Primarily concerns, the solving the issue of the : Principle Principal of David Lewis, in all of its forms, as qualitative, numerical, qualitative (Actualist) and numerical Actualist PP.

-And the interpretation and foundation of the concept of 'probability".

Propensities as the truth-makers of the world needed to facilitate the strange mind-to world connection required to connect propensity to their required connection to conditional logic, and the doxastic attitudes of agents, in order to answer the challenge of the Principal Principle.

**I try to answer at very least this questions:**

$$PP_{1}:\text{numerical, non-Actualist Principle Principal often call the Principal Principle}.$$

**$$PP_{1}:Cr(A|PR(A)=x)=x$$**

"Why is one (guaranteed to be?) better, off, on the single case, using the single case alone, without indifference or relative frequency principles, having one's subjective probabilities, denoted/credences denoted: $Cr$, aligned with aligned with the objective chance . values/probabilities denoted: $PR$? - Where by "more"- I mean that this is graded, via dominance/logic, alone, in the sense of:

$$\subset|\equiv|\supset|\leftrightarrow|\to|\leftarrow.$$

And justified in terms of dominance alone, vis a vis conditional beliefs in virtue of the underlying objective single case propensity account that I develop using a weird resistance concept to facilitate the required mind-world connection.

$$PR(A)>PR(B) \iff [A\supset B].$$

$$\text{or more generally}:$$

$$[PR(A)>PR(B)] \iff [A\to B].$$

$$PR(A)=PR(B)\iff\[A\leftrightarrow B].$$

Which is meant to taken literally in my account of probability. Including, but not limited to, the case of two equi-probable and thus "logically equivalent, yet, mutually exclusive and exhaustive, events: $$\frac{1}{2}=PR(A)=PR(¬A)\iff [A↔¬A].$$