Labelled Natural Deduction Systems for Quantified Modal Logics

2000 ◽  
pp. 91-113
Author(s):  
Luca Viganò
Keyword(s):  
Natural Deduction ◽  
Modal Logics

Label-free natural deduction systems for intuitionistic and classical modal logics

2010 ◽  
Vol 20 (4) ◽  
pp. 373-421 ◽  
Author(s):  
Didier Galmiche ◽  
Yakoub Salhi
Keyword(s):  
Natural Deduction ◽  
Modal Logics ◽  
Label Free

scholarly journals From 2-Sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics

2021 ◽  
Vol 22 (3) ◽  
pp. 1-29
Author(s):  
Simone Martini ◽  
Andrea Masini ◽  
Margherita Zorzi
Keyword(s):  
Natural Deduction ◽  
Modal Logics ◽  
Structural Rule ◽  
Elimination Rule ◽  
Accessibility Relation ◽  
Formal Systems ◽  
Explicit Reference ◽  
Deduction Rules ◽  
Nested Sequents ◽  
Normal Modal Logics

We extend to natural deduction the approach of Linear Nested Sequents and of 2-Sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction: only one introduction and one elimination rule per connective, no additional (structural) rule, no explicit reference to the accessibility relation of the intended Kripke models. We give systems for the normal modal logics from K to S4. For the intuitionistic versions of the systems, we define proof reduction, and prove proof normalization, thus obtaining a syntactical proof of consistency. For logics K and K4 we use existence predicates (à la Scott) for formulating sound deduction rules.

scholarly journals Natural deduction rules for modal logics.

1972 ◽  
Vol 13 (4) ◽  
pp. 461-475 ◽  
Author(s):  
Thomas W. Satre
Keyword(s):  
Natural Deduction ◽  
Modal Logics ◽  
Deduction Rules

Modal logics with Belnapian truth values

2010 ◽  
Vol 20 (3) ◽  
pp. 279-304 ◽  
Author(s):  
Serge P Odintsov ◽  
Heinrich Wansing
Keyword(s):  
Modal Logics ◽  
Truth Values

Suppose and Tell

2020 ◽  
Author(s):  
Timothy Williamson
Keyword(s):  
Conditional Probability ◽  
Natural Deduction ◽  
Special Kind ◽  
Context Sensitivity ◽  
Modal Operator ◽  
Counterfactual Conditionals ◽  
Deduction Rules ◽  
Psychological Sense

The book argues that our use of conditionals is governed by imperfectly reliable heuristics, in the psychological sense of fast and frugal (or quick and dirty) ways of assessing them. The primary heuristic is this: to assess ‘If A, C’, suppose A and on that basis assess C; whatever attitude you take to C conditionally on A (such as acceptance, rejection, or something in between) take unconditionally to ‘If A, C’. This heuristic yields both the equation of the probability of ‘If A, C’ with the conditional probability of C on A and standard natural deduction rules for the conditional. However, these results can be shown to make the heuristic implicitly inconsistent, and so less than fully reliable. There is also a secondary heuristic: pass conditionals freely from one context to another under normal conditions for acceptance of sentences on the basis of memory and testimony. The effect of the secondary heuristic is to undermine interpretations on which ‘if’ introduces a special kind of context-sensitivity. On the interpretation which makes best sense of the two heuristics, ‘if’ is simply the truth-functional conditional. Apparent counterexamples to truth-functionality are artefacts of reliance on the primary heuristic in cases where it is unreliable. The second half of the book concerns counterfactual conditionals, as expressed with ‘if’ and ‘would’. It argues that ‘would’ is an independently meaningful modal operator for contextually restricted necessity: the meaning of counterfactuals is simply that derived compositionally from the meanings of their constituents, including ‘if’ and ‘would’, making them contextually restricted strict conditionals.

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