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

100%
Rönnedal D.
Logic and Logical Philosophy
|
2018
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vol. 27
|
issue 1
3–52
EN
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.
2

Quantified temporal alethic-deontic logic

100%
Rönnedal D.
Logic and Logical Philosophy
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2015
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vol. 24
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issue 1
19–59
EN
The purpose of this paper is to describe a set of quantified temporal alethic-deontic systems, i.e., systems that combine temporal alethicdeontic logic with predicate logic. We consider three basic kinds of systems: constant, variable and constant and variable domain systems. These systems can be augmented by either necessary or contingent identity, and every system that includes identity can be combined with descriptors. All logics are described both semantically and proof theoretically. We use a kind of possible world semantics, inspired by the so-called T × W semantics, to characterize them semantically and semantic tableaux to characterize them proof theoretically. We also show that all systems are sound and complete with respect to their semantics.
3

BOULESIC LOGIC, DEONTIC LOGIC AND THE STRUCTURE OF A PERFECTLY RATIONAL WILL

100%
Rönnedal D.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2020
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vol. 27
|
issue 2
187 – 262
EN
In this paper, I will discuss boulesic and deontic logic and the relationship between these branches of logic. By ‘boulesic logic,’ or ‘the logic of the will,’ I mean a new kind of logic that deals with ‘boulesic’ concepts, expressions, sentences, arguments and systems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be the case that’ and ‘individual x accepts that it is the case that.’ These expressions will be symbolised by two sentential operators that take individuals and sentences as arguments and give sentences as values. Deontic logic is a relatively well-established branch of logic. It deals with normative concepts, sentences, arguments and systems. In this paper, I will show how deontic logic can be grounded in boulesic logic. I will develop a set of semantic tableau systems that include boulesic and alethic operators, possibility quantifiers and the identity predicate; I will then show how these systems can be augmented by a set of deontic operators. I use a kind of possible world semantics to explain the intended meaning of our formal systems. Intuitively, we can think of our semantics as a description of the structure of a perfectly rational will. I mention some interesting theorems that can be proved in our systems, including some versions of the so-called hypothetical imperative. Finally, I show that all systems that are described in this paper are sound and complete with respect to their semantics.
4

SEMANTIC TABLEAU VERSIONS OF SOME NORMAL MODAL SYSTEMS WITH PROPOSITIONAL QUANTIFIERS

100%
Rönnedal D.
Organon F. medzinárodný časopis pre analytickú filozofiu
|
2019
|
vol. 26
|
issue 3
505 - 536
EN
In Symbolic Logic (1932), C. I. Lewis developed five modal systems S1 − S5. S4 and S5 are so-called normal modal systems. Since Lewis and Langford’s pioneering work many other systems of this kind have been investigated, among them the 32 systems that can be generated by the five axioms T, D, B, 4 and 5. Lewis also discusses how his systems can be augmented by propositional quantifiers and how these augmented logics allow us to express some interesting ideas that cannot be expressed in the corresponding quantifier-free logics. In this paper, I will develop 64 normal modal semantic tableau systems that can be extended by propositional quantifiers yielding 64 extended systems. All in all, we will investigate 128 different systems. I will show how these systems can be used to prove some interesting theorems and I will discuss Lewis’s so-called existence postulate and some of its consequences. Finally, I will prove that all normal modal systems are sound and complete and that all systems (including the extended systems) are sound with respect to their semantics. It is left as an open question whether or not the extended systems are complete.
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