Some Theorems about a “Tree” System of Deontic Tense Logic

Åqvist, Lennart; Hoepelman, Jaap

doi:10.1007/978-94-009-8484-4_9

Cited by 40 publications

(22 citation statements)

References 14 publications

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“…1 We regret being unable in this article to discuss Hansson's own solution to the epistemic obligation paradox as proposed in his paper Hansson (2003), where he suggests that deontic logic be based directly on a preference relation, according to the principle that whatever is better than something permitted is itself permitted. Also, strangely enough, in the joint paper Åqvist and Hoepelman (1981) in Hilpinen (1981) I seem completely to have overlooked the solution to the puzzle for which I argue here -this is strange, because the crucial Lemma, on which my present solution is based, was in all essentials stated and proved already in that old joint paper (see section 12 of Åqvist and Hoepelman, 1981). By T8, then, the "monadic" O modality (= O T ) is vacuous or collapses into ("reduces to") its argument when the latter contains no operators or constants of the kinds stated in the proviso.…”

Section: B)mentioning

confidence: 99%

Deontic Tense Logic With Historical Necessity, Frame Constants, and a Solution to the Epistemic Obligation Paradox (The “Knower”)

Åqvist

2014

Theoria

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In an earlier paper by the author, Åqvist (1999), I presented an approach to the logic of historical necessity, or inevitability, in the sense of a "two-dimensional" combination of tense and modal logic for worlds, or histories, with the same time order, known as T × W logic. Distinctive features of that approach were, apart from its two-dimensionality, its being based on discrete and finite time, and its use of so-called systematic frame constants in order to enable us to indicate longitudes (x-values) and latitudes (y-values) of any points in the co-ordinate systems under consideration. This led us to study and axiomatize an infinite hierarchy HTWxy of two-dimensional modal tense logics with the characteristic operators for historical necessity and possibility added to the original basic vocabulary. The main purpose of the present paper is then twofold: (A) to extend the logics HTWxy to the interesting branch of philosophical logic constituted by deontic logic as combined with tense (or temporal) logic; and (B) to deal with a curious puzzle known as the so-called epistemic obligation paradox -a well known stumbling-block in this area of research in philosophical logic. We argue for a solution to both these problems, which appeals to a new infinite hierarchy DHTWxym of extensions of the HTWxy in the sense of logics combining dyadic deontic modalities with temporal ones such as those for historical necessity and other two-dimensional modalities.

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Section: B)mentioning

confidence: 99%

Deontic Tense Logic With Historical Necessity, Frame Constants, and a Solution to the Epistemic Obligation Paradox (The “Knower”)

Åqvist

2014

Theoria

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“…Several philosophers and logicians have developed logical systems that deal with various combinations of the conditions governing temporal, alethic and deontic elements (e.g. Chellas [14], Bailhache [3,4,5,6], van Eck [51], Thomason [48,49], Åqvist and Hoepelman [68], Åqvist [67], Bartha [7], Horty [30], Belnap, Perloff and Xu [8], Brown [9,10,11]). However, as far as we know, no one has developed any tableau systems of the kind introduced in this paper.…”

Section: O[a]b O(a → B)mentioning

confidence: 99%

“…[3,4,5,6,14,50,68,67]), momentbased (branching time) semantics (e.g. [7,30,8]) and branch-based semantics (e.g.…”

Section: O[a]b O(a → B)mentioning

confidence: 99%

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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“…Some authors have proposed to avoid the inconsistency of between (6.4) and (6.7) by relativizing the concept of obligation (or the concept of ought) time: it has been suggested that (6.4) and (6.7) hold at different points of time (Åqvist and Hoepelman 1981). It is obvious that what is obligatory or permitted changes over time; thus it is natural to assume, quite independently of the paradox of contrary-to-duty obligation, that deontic concepts should be analyzed by means of temporally structured systems of possible worlds, and that deontic logic should be based on tense logic (Thomason 1981(Thomason , 1984Horty 2001).…”

Section: Temporal Framesmentioning

confidence: 99%

Deontic, Epistemic, and Temporal Modal Logics

Hilpinen¹

2006

A Companion to Philosophical Logic

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Modal ConceptsModalities (necessity, possibility, and related concepts and expressions) can be interpreted in different ways: for example, the possibility of a proposition or a state of affairs can be taken to mean that it is not ruled out by what is known (an epistemic interpretation) or believed (a doxastic interpretation), or that it is not ruled out by the accepted legal or moral requirements (a deontic interpretation), or that it has not always been or will not always be false (a temporal interpretation). These interpretations are sometimes contrasted with alethic modalities, which are thought to express the ways ('modes') in which a proposition can be true or false. For example, logical possibility and physical (real or substantive) possibility are alethic modalities.The basic modal concepts are represented in systems of modal logic as propositional operators; thus they are regarded as syntactically analogous to the concept of negation and other propositional connectives. The main difference between modal operators and other connectives is that the former are not truth-functional; the truth-value (truth or falsity) of a modal sentence is not determined by the truth-values of its subsentences. The concept of possibility ('it is possible that' or 'possibly') is usually symbolized by ‡ and the concept of necessity ('it is necessary that' or 'necessarily') by ᮀ; thus the modal formula ‡p represents the sentence form 'it is possible that p' or 'possibly p,' and ᮀp should be read 'it is necessary that p.' Modal operators can be defined in terms of each other: 'it is possible that p' means the same as 'it is not necessary that not-p'; thus ‡p can be regarded as an abbreviation of ÿᮀÿp, where ÿ is the sign of negation, and ᮀp is logically equivalent to ÿ ‡ÿp. Systems modal propositional logic or quantification theory (predicate logic) are obtained by adding the symbols ‡ and ᮀ (and possibly other modal signs), together with appropriate rules of sentence formation (e.g. if A is a formula, ‡A and ᮀA are formulas), to a system of (non-modal) propositional logic or quantification theory.

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Some Theorems about a “Tree” System of Deontic Tense Logic

Cited by 40 publications

References 14 publications

Deontic Tense Logic With Historical Necessity, Frame Constants, and a Solution to the Epistemic Obligation Paradox (The “Knower”)

Deontic Tense Logic With Historical Necessity, Frame Constants, and a Solution to the Epistemic Obligation Paradox (The “Knower”)

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

Deontic, Epistemic, and Temporal Modal Logics

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