Trivializing Informational Consequence

Santorio, Paolo

doi:10.1111/phpr.12745

Cited by 9 publications

(2 citation statements)

References 70 publications

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“…The fact that McGee's argument is analyzed as valid in C and as invalid in U is also in accordance with the ambivalence generally felt regarding whether the argument is valid or not. Similar distinctions between the validity of Modus Ponens in certain and uncertain inference are, in different frameworks, defended byNeth (2019) andSantorio (2022).…”

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confidence: 68%

Certain and Uncertain Inference with Trivalent Conditionals

Égré¹,

Rossi²,

Sprenger³

2022

Preprint

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Research on indicative conditionals usually aims either at determining their truth conditions, or at explaining how we should reason with them and when we can assert them. This paper integrates these semantic and epistemological projects by means of articulating trivalent, truthfunctional truth conditions for indicative conditionals. Based on this framework, we provide a (non-classical) account of the probability of conditionals, and two logics of conditional reasoning: (i) a logic C of inference from certain premises that generalizes deductive reasoning; and (ii) a logic U of inference from uncertain premises that generalizes defeasible reasoning. Both logics are highly attractive in their domain. They provide a unified framework for conditional reasoning, generalize existing theories (e.g., Adams's logic of "reasonable inference") and yield an insightful analysis of the controversies about the validity of Modus Ponens, Import-Export and other principles of conditional logic.

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confidence: 68%

Certain and Uncertain Inference with Trivalent Conditionals

Égré¹,

Rossi²,

Sprenger³

2022

Preprint

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“…But McGee [104] has famously argued that one can assign higher probability to p ∧ (p → (q → r)) than to q → r, so the former does not entail the latter (cf. [105] (Section 4)). On the other hand, if instead of trying to capture a notion of entailment with respect to which probability is monotonic, we try to capture preservation of probability 1, then Modus Ponens seems unimpeachable: if the probability of ϕ is 1 and the probability of ϕ → ψ is 1, then the probability of ψ should be 1 as well.…”

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confidence: 99%

A Fundamental Non-Classical Logic

Holliday

2023

Logics

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We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation. Finally, we discuss ways of extending these representations to lattices with a conditional or implication operation.

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Acceptance and Certainty, Doxastic Modals, and Indicative Conditionals

Norlin¹

2022

J Philos Logic

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Trivializing Informational Consequence

Cited by 9 publications

References 70 publications

Certain and Uncertain Inference with Trivalent Conditionals

Certain and Uncertain Inference with Trivalent Conditionals

A Fundamental Non-Classical Logic

Acceptance and Certainty, Doxastic Modals, and Indicative Conditionals

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