Alethic Modal Logics and Semantics

Schurz, Gerhard

doi:10.1002/9780470996751.ch30

Cited by 3 publications

(2 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally we mention that an equivalent translation of QL is also possible into predicate logic instead of DQL, since it is well known from modal correspondence theory that every modal formula can be equivalently translated into a formula of first or higher order predicate logic (cf. [57], sec. 2.3).…”

Section: Two Possibilities Of Translating Quantum Logicsmentioning

confidence: 99%

Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism

Schurz

2021

J Philos Logic

Self Cite

View full text Add to dashboard Cite

In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value (sec. 1). Is a non-circular justification of a logical system possible? This question attains particular importance in view of lasting controversies about classical versus non-classical logics. In this paper the question is answered positively, based on meaning-preserving translations between logical systems. It is demonstrated that major systems of non-classical logic, including multi-valued, paraconsistent, intuitionistic and quantum logics, can be translated into classical logic by introducing additional intensional operators into the language (sec. 2–5). Based on this result it is argued that classical logic is representationally optimal. In sec. 6 it is investigated whether non-classical logics can be likewise representationally optimal. The answer is predominantly negative but partially positive. Nevertheless the situation is not symmetric, because classical logic has important ceteris paribus advantages as a unifying metalogic.

show abstract

Section: Two Possibilities Of Translating Quantum Logicsmentioning

confidence: 99%

Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism

Schurz

2021

J Philos Logic

Self Cite

View full text Add to dashboard Cite

show abstract

“…See(Schurz 2002).18 From the point of view of the logical language, SQML requires us to extend FOL language so that the necessity modal operator □ is added: if  is a formula, then □ is also a formula. The possibility operator ◊ is defined as usual: ◊ =def □.…”

mentioning

confidence: 99%

A Formal-Logical Approach to the Concept of God

Silvestre

2021

Manuscrito

View full text Add to dashboard Cite

In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing logical formalism. I start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory 1 This paper is part of the project "The Rationality of Theistic Belief and the Plausibility of the Concept of God", sponsored by the John Templeton Foundation under its umbrella project "Supporting Constructive Research on the Existence of God in Portuguese-Speaking Latin America".

show abstract

Possible Worlds Semantics for Indicative and Counterfactual Conditionals?

Unterhuber¹

2013

View full text Add to dashboard Cite

Alethic Modal Logics and Semantics

Cited by 3 publications

References 54 publications

Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism

Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism

A Formal-Logical Approach to the Concept of God

Possible Worlds Semantics for Indicative and Counterfactual Conditionals?

Contact Info

Product

Resources

About