791 research outputs found
Conditionals and modularity in general logics
In this work in progress, we discuss independence and interpolation and
related topics for classical, modal, and non-monotonic logics
A Puzzle about Knowing Conditionals
We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a conditional from a disjunction
A 4-valued logic of strong conditional
How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions (Section 1), we argue that a stronger account of conditional can be obtained in two steps: firstly, by reminding its historical roots inside modal logic and set-theory (Section 2); secondly, by revising the meaning of logical values, thereby getting rid of the paradoxes of material implication whilst showing the bivalent roots of conditional as a speech-act based on affirmations and rejections (Section 3). Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed through a broader definition of logical consequence that encompasses both a normal relation of truth propagation and a weaker relation of falsity non-propagation from premises to conclusion (Section 3)
Subjective probability, trivalent logics and compound conditionals
In this work we first illustrate the subjective theory of de Finetti. We
recall the notion of coherence for both the betting scheme and the penalty
criterion, by considering the unconditional and conditional cases. We show the
equivalence of the two criteria by giving the geometrical interpretation of
coherence. We also consider the notion of coherence based on proper scoring
rules. We discuss conditional events in the trivalent logic of de Finetti and
the numerical representation of truth-values. We check the validity of selected
basic logical and probabilistic properties for some trivalent logics:
Kleene-Lukasiewicz-Heyting-de Finetti; Lukasiewicz; Bochvar-Kleene; Sobocinski.
We verify that none of these logics satisfies all the properties. Then, we
consider our approach to conjunction and disjunction of conditional events in
the setting of conditional random quantities. We verify that all the basic
logical and probabilistic properties (included the Fr\'{e}chet-Hoeffding
bounds) are preserved in our approach. We also recall the characterization of
p-consistency and p-entailment by our notion of conjunction
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