Quantified temporal alethic-deontic logic

Rönnedal, Daniel

doi:10.12775/llp.2014.016

Cited by 5 publications

(29 citation statements)

References 31 publications

(41 reference statements)

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“…We use the same conditions on the alethic accessibility relation R, and the temporal accessibility relation < as in [44] and [46]. Intuitively, it is often reasonable to treat the alethic accessibility relation R as an equivalence relation.…”

Section: Conditions On Frames and Modelsmentioning

confidence: 99%

“…The conditions concerning the relation between R, < and V (see Table 4) are exactly the same as in [44] and [46]. C-SP, C-FT and C-BT correspond to the tableau rules T -SP, T -FT and T -BT (see Table 11).…”

Section: Conditions Concerning the Relation Between R < And Vmentioning

confidence: 99%

“…Melvin Fitting and Graham Priest [24,25,38]. The concepts of semantic tableau, branch, open and closed branch, etc., are essentially defined as in [44,46,38]. For more information on semantic tableaux, see D'Agostino, Gabbay, Hähnle and Posegga [19].…”

Section: Proof Theory 41 Semantic Tableauxmentioning

confidence: 99%

“…Many rules that we use in temporal alethic dyadic deontic logic are described by [44] and [46]. In addition, we will consider some new tableau rules for the dyadic deontic operators and some new rules that "correspond to" the conditions imposed on the dyadic deontic accessibility relations that were introduced in Section 3.2.…”

Section: Tableau Rulesmentioning

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: Conditions On Frames and Modelsmentioning

confidence: 99%

Section: Conditions Concerning the Relation Between R < And Vmentioning

confidence: 99%

Section: Proof Theory 41 Semantic Tableauxmentioning

confidence: 99%

Section: Tableau Rulesmentioning

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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Contrary-to-Duty Paradoxes and Counterfactual Deontic Logic

Rönnedal

2019

Philosophia

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In this paper, I will discuss some examples of the so-called contrary-to-duty (obligation) paradox, a well-known puzzle in deontic logic. A contrary-to-duty obligation is an obligation telling us what ought to be the case if something forbidden is true, for example: 'If she is guilty, she should confess'. Contrary-to-duty obligations are important in our moral and legal thinking. Therefore, we want to be able to find an adequate symbolisation of such obligations in some logical system, a task that has turned out to be difficult. This is shown by the so-called contrary-to-duty (obligation) paradox. I will investigate and evaluate one kind of solution to this problem that has been suggested in the literature, which I will call the 'counterfactual solution'. I will use some recent systems that combine not only counterfactual logic and deontic logic, but also temporal logic, in my analysis of the paradox. I will argue that the counterfactual solution has many attractive features and that it can give a fairly satisfactory answer to some examples of the contrary-to-duty paradox, but that it nevertheless has some serious problems. The conclusion is that, notwithstanding the many attractive features of the solution, there seem to be other approaches to the paradox that are more promising.

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Árboles semánticos para algunas lógicas alético-epistémico-doxásticas

Hernández

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Omitiré paréntesis donde no haya ambigüedad. ∨, ⊃, ≡, 3, , ⊤ y ⊥ se definen como es usual. p | q = def ¬(p ∧ q), y se lee 'p es incompatible con q'.Un modelo de Kripke para interpretar a L A es una tupla ⟨W , R, ν⟩. W es un conjunto no vacío de mundos posibles. Hablaré un poco sobre estos en los capítulos 2, 4 y 5. R es una relación binaria de accesibilidad, R ⊆ W × W , de forma que Rww ′ significa que w accede a w ′ . 2 ν es una función de tuplas de mundos posibles y parámetros proposicionales al conjunto de valores clásicos de verdad, ν : W × P → {1, 0}, de forma que ν w (p) = 1 quiere decir que en w, p es verdadera.Las condiciones de verdad de los elementos de L A son las siguientes:Sea Σ un conjunto de fórmulas bien formadas. La validez semántica (|=) se define por la preservación de la verdad a través de mundos:Para la validez sintáctica o teoría de la demostración, ⊢, podemos usar tanto sistemas axiomáticos como de árboles. En este capítulo, sólo veré aproximaciones axiomáticas.El sistema axiomático de K 2 consta de:(LC) Todos los axiomas y teoremas, ⊢ φ, de la lógica clásica proposicional (SU) Si ⊢ φ y p forma parte de φ, entonces la fórmula resultante, φ ′ , al sustituir uniformemente p por ψ, [p/ψ], también es válida,(MP) es modus ponens para el condicional material. (N2) se conoce como la regla de necesariedad (alética), e indica que una verdad lógica (analítica) es una verdad necesaria. Si φ es una verdad lógica, φ es verdadera en cualquier mundo posible en el que se le evalúe. (C2) se conoce como el principio de cerradura, es el axioma característico de K 2 y es válido en todas las lógicas modales normales. 3 9 Que las creencias pueden ser falsas, pero no el conocimiento, puede rastrearse hasta Platón (Gor-

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Quantified temporal alethic-deontic logic

Cited by 5 publications

References 31 publications

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

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

Contrary-to-Duty Paradoxes and Counterfactual Deontic Logic

Árboles semánticos para algunas lógicas alético-epistémico-doxásticas

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