Dyadic deontic logic and semantic tableaux

Rönnedal, Daniel

doi:10.12775/llp.2009.011

Cited by 5 publications

(27 citation statements)

References 20 publications

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“…The systems developed in this essay are modifications and extensions of the dyadic deontic systems and temporal alethic-deontic systems introduced by Rönnedal [43] and Rönnedal [44]. (See also Rönnedal [46].)…”

Section: Introductionmentioning

confidence: 99%

“…This accessibility relation plays an important part in the formulation of the alternative truth conditions for the various normative sentences introduced in Section 3.1.3. [43] does not include any alethic accessibility relation. Secondly, in our so-called supplemented frames and models, we relativise our preference relation between possible worlds to possible worlds; i.e., our preference relation between possible worlds is treated as a ternary relation in this paper, not as a binary relation as in [43].…”

Section: Introductionmentioning

confidence: 99%

“…[43] does not include any alethic accessibility relation. Secondly, in our so-called supplemented frames and models, we relativise our preference relation between possible worlds to possible worlds; i.e., our preference relation between possible worlds is treated as a ternary relation in this paper, not as a binary relation as in [43]. The reason for this is connected to the fact that we do not assume that every possible world is alethically accessible from every possible world (at every moment of time) (see Section 3.2.3).…”

Section: Introductionmentioning

confidence: 99%

“…Cα3 , C-Dα3 in this paper) and tableau rules (e.g. T α3 , T -Dα3 in this paper) introduced by [43] and [44]; we have to delete some semantic conditions (e.g. Ca6 ) and also add some new conditions (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…T -DMO) to our systems (sections 3 and 4). In addition, we consider some tableau rules that do not have any counterparts in [43], [44] or [46] (T -Dd4 , T -Dd5 , T -Dd7 , T -Dad4 , T -Dad5 ) and we prove several interesting theorems. We can, for example, show that all of the following conditional obligations are equivalent in some systems (see Section 5):…”

Section: Introductionmentioning

confidence: 99%

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Temporal Alethic Dyadic Deontic Logic and the Contrary-to-Duty Obligation Paradox

Rönnedal

2017

LLP

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Abstract.A contrary-to-duty obligation (sometimes called a reparational duty) is a conditional obligation where the condition is forbidden, e.g. "if you have hurt your friend, you should apologise", "if he is guilty, he should confess", and "if she will not keep her promise to you, she ought to call you". It has proven very difficult to find plausible formalisations of such obligations in most deontic systems. In this paper, we will introduce and explore a set of temporal alethic dyadic deontic systems, i.e., systems that include temporal, alethic and dyadic deontic operators. We will then show how it is possible to use our formal apparatus to symbolise contrary-to-duty obligations and to solve the so-called contrary-to-duty (obligation) paradox, a problem well known in deontic logic. We will argue that this response to the puzzle has many attractive features. Semantic tableaux are used to characterise our systems proof theoretically and a kind of possible world semantics, inspired by the so-called T × W semantics, to characterise them semantically. Our models contain several different accessibility relations and a preference relation between possible worlds, which are used in the definitions of the truth conditions for the various operators. Soundness results are obtained for every tableau system and completeness results for a subclass of them.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Temporal Alethic Dyadic Deontic Logic and the Contrary-to-Duty Obligation Paradox

Rönnedal

2017

LLP

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Transgressions Are Equal, and Right Actions Are Equal: some Philosophical Reflections on Paradox III in Cicero’s Paradoxa Stoicorum

Rönnedal

2016

Philosophia

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In Paradoxa Stoicorum, the Roman philosopher Cicero defends six important Stoic theses. Since these theses seem counterintuitive, and it is not likely that the average person would agree with them, they were generally called “paradoxes”. According to the third paradox, (P3), (all) transgressions (wrong actions) are equal and (all) right actions are equal. According to one interpretation of this principle, which I will call (P3′), it means that if it is forbidden that A and it is forbidden that B, then not-A is as good as not-B; and if it is permitted that A and it is permitted that B, then A is as good as B. In this paper, I show how it is possible to prove this thesis in dyadic deontic logic. I also try to defend (P3′) against some philosophical counterarguments. Furthermore, I address the claim that (P3′) is not a correct interpretation of Cicero’s third paradox and the assertion that it does not matter whether (P3′) is true or not. I argue that it does matter whether (P3′) is true or not, but acknowledge that (P3′) is perhaps a slightly different principle than Cicero’s thesis. The upshot is that (P3′) seems to be a plausible principle, and that at least one part of paradox III in Cicero’s Paradoxa Stoicorum appears to be defensible.

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