Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probability Distinguishes Different Types of Conditional Statements   The language of probability is used to define several different types of
conditional statements. There are four principal types: subjunctive, material,
existential, and feasibility. Two further types of conditionals are defined
using the propositional calculus and Boole's mathematical logic:
truth-functional and Boolean feasibility (which turn out to be special cases of
probabilistic conditionals). Each probabilistic conditional is quantified by a
fractional parameter between zero and one that says whether it is purely
affirmative, purely negative, or intermediate in its sense. Conditionals can be
specialized further by their content to express factuality and
counterfactuality, and revised or reformulated to account for exceptions and
confounding factors. The various conditionals have distinct mathematical
representations: through intermediate probability expressions and logical
formulas, each conditional is eventually translated into a set of polynomial
equations and inequalities (with real coefficients). The polynomial systems
from different types of conditionals exhibit different patterns of behavior,
concerning for example opposing conditionals or false antecedents. Interesting
results can be computed from the relevant polynomial systems using well-known
methods from algebra and computer science. Among other benefits, the proposed
framework of analysis offers paraconsistent procedures for logical deduction
that produce such familiar results as modus ponens, transitivity, disjunction
introduction, and disjunctive syllogism; all while avoiding any explosion of
consequences from inconsistent premises. Several example problems from Goodman
and Adams are analyzed. A new perspective called polylogicism is presented:
mathematical logic that respects the diversity among conditionals in particular
and logic problems in general.

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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: stat