arXiv subjects

Jan Sprenger

Publications and source records attributed to Jan Sprenger.

4 recordsLinked to original sources

arXiv2023

Certain and Uncertain Inference with Indicative Conditionals

This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by W. Cooper and yields two logics of conditional reasoning: (i) a logic C of inference from certain premises; and (ii) a logic U of inference from uncertain premises. But whereas C is monotonic for the conditional, U is not, and whereas C obeys Modus Ponens, U does not without restrictions. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, and we use the distinction between the two systems to cast light, in particular, on McGee's puzzle about Modus Ponens. The result is a unified account of the semantics and epistemology of indicative conditionals that can be fruitfully applied to analyzing the validity of conditional inferences.

cs.AI↗

arXiv2023

Causal Modeling Semantics for Counterfactuals with Disjunctive Antecedents

Causal Modeling Semantics (CMS, e.g., Galles and Pearl 1998; Pearl 2000; Halpern 2000) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual (A v B) > C at a causal model M as a weighted average of the probability of C in those submodels that truthmake A v B (Briggs 2012; Fine 2016, 2017). The weights of the submodels are given by the inverse distance to the original model M, based on a distance metric proposed by Eva, Stern, and Hartmann (2019). Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined.

cs.LO↗

arXiv2020

Gibbardian Collapse and Trivalent Conditionals

This paper discusses the scope and significance of the so-called triviality result stated by Allan Gibbard for indicative conditionals, showing that if a conditional operator satisfies the Law of Import-Export, is supraclassical, and is stronger than the material conditional, then it must collapse to the material conditional. Gibbard's result is taken to pose a dilemma for a truth-functional account of indicative conditionals: give up Import-Export, or embrace the two-valued analysis. We show that this dilemma can be averted in trivalent logics of the conditional based on Reichenbach and de Finetti's idea that a conditional with a false antecedent is undefined. Import-Export and truth-functionality hold without triviality in such logics. We unravel some implicit assumptions in Gibbard's proof, and discuss a recent generalization of Gibbard's result due to Branden Fitelson.

math.LO↗

arXiv2019

De Finettian Logics of Indicative Conditionals

This paper explores trivalent truth conditions for indicative conditionals, examining the "defective" table put forward by de Finetti 1936, as well as Reichenbach 1944, first sketched in Reichenbach 1935. On their approach, a conditional takes the value of its consequent whenever its antecedent is True, and the value Indeterminate otherwise. Here we deal with the problem of choosing an adequate notion of validity for this conditional. We show that all standard trivalent schemes are problematic, and highlight two ways out of the predicament: one pairs de Finetti's conditional (DF) with validity as the preservation of non-False values (TT-validity), but at the expense of Modus Ponens; the other modifies de Finetti's table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti's table (CC) proposed by Cooper 1968 and Cantwell 2008. In Part II, we give an in-depth treatment of the proof theory of the resulting logics, DF/TT and CC/TT: both are connexive logics, but with significantly different algebraic properties.

math.LO↗