Deontic Logic
What fish is this?
1. Deontic Logic is so mysterious that there isn't even an easy answer to what's it all about. Some would say its subject are the relations between the ordinary language modal operators 'It is obligatory that ...', 'It is forbidden that ...', 'It is permitted that ...', usually formalized as OA, FA, PA, which deontic logic classically treats as analogous to the so-called 'alethic' modalities 'It is necessary that ...', 'It is impossible that ...', 'It is possible that ...'. There is then a dispute on whether the '...' part is to be a factual description like 'the window is closed', an action sentence 'Jörg closes the window', or just anything. Others would more broadly say the subject of deontic logic is the logic of legal or moral discourse (or both), and some like to extend it to the use of imperatives even in scientific discourse ("Let alpha equal zero!").
If you just strolled across this site by means of a search engine, be warned: There are, nowadays, a hundreds of publications on deontic logic. For a good introduction, read Risto Hilpinen's collections "Deontic Logic" (1971) and "New Studies in Deontic Logic" (1981). The best known system of deontic logic is the modal system D, also called 'standard deontic logic' or SDL. But SDL has problems formalizing conditional obligations, and cannot formalize contrary-to-duty obligations (e.g. don't smoke, but if you do at least use an ash-tray). This was the reason why its own authors, Georg Henrik von Wright and Arthur N. Prior, gave up SDL in 1956 in favor of a dyadic approach, that formalizes 'It is obligatory that ... under the condition ...' as O(A/C). Dyadic deontic logic has often been linked to preference reasoning (the best thing, given the situation I am in, or the choice I have, is ...). Dyadic deontic logic has also been linked to non-monotonic logic, since the obligations may change when the circumstances do (e.g. in an example by Plato, a man must return the weapon he borrowed, but not when the lender has become mad or is drunk). One of the strongest dyadic deontic systems is Lennart Åqvist's system G, based on Bengt Hansson's DSDL3. Other people have used settings of temporal logic, of relevant logic or dynamic logic to explain their deontic logic. Even though none of the systems that exist today seems to be free of counterintuitive results (the so-called 'paradoxes of deontic logic'), stopping at SDL would scarcely be state of the art anymore. So please find your way into the literature before you condemn the whole enterprise.
On biannual DEON workshops philosophers, jurists, mathematicians, and computer scientists exchange their views. The next workshop will be held 12-14 July 2006, Utrecht Universität, Netherlands, Europe - visit the DEON 2006 homepage.
2. I provide some papers of mine below. Tell me what you think of them.
Contribution to the Colloquium 'Action, Norms, Values', ZiF Bielefeld
1996. Appeared in: G. Meggle (ed.), Actions, Norms, Values: Discussions
with Georg Henrik von Wright, de Gruyter: Berlin, 1998, pp 255-263.)
Abstract: Professor von Wright's logic of
norms as developed by him since 1981 is examined for paradoxes of commitment.
In this logic the basic form of conditional norms is 'O(p -> q)'. It
is shown that Chisholm's Paradox does not arise in this logic and that some
Roman arguments concerning conditional promises can be reconstructed by
it. Finally an example is presented which suggests that conditional obligation
cannot generally be represented by 'O(p -> q)'.
Contribution to the DEON
'98 workshop. Appeared in: H. Prakken, P. McNamara (eds.), Norms, Logics,
and Information Systems, IOS Press: Amsterdam, 1999, pp.127-144.
Abstract: The aim of this essay is to tie
up some loose ends in deontic logic. Under consideration are two particularly
strong deontic systems: Åqvist's dyadic deontic logic G and van Eck's
system of temporally relative deontic logic. From van Eck's system of quantificational
deontic temporal logic QDTL a corresponding propositional deontic temporal
system DTL is constructed to which Arrow's Axiom is added and the resulting
system called DTL+. I prove we can translate G-sentences into DTL-sentences
such that any translated theorem of G is a valid sentence of DTL+ and any
sentence of DTL that is such a translation and is valid in DTL+ is valid
in G also. Metaphorically speaking, stan-dard dyadic deontic logic as represented
by G is the logic of a snap shot picturing the deontic relations between
world courses in a DTL+-model at any point of time.
Notes to my DEON '98 contribution (zipped postscript, 385 kB, pdf 444 kB). Some notes to the DEON '98 contribution in an Q&A style, and some further proofs as well as one that failed.
Contribution to the DEON '00
workshop. Appeared in Fundamenta Informaticae 48 (2001), 205-226.
Abstract: Though deontic logic is regarded
as the logic of normative reasoning, norms - as entities lacking truth values
- are usually represented neither in its language nor its semantics. Limiting
ourselves to unconditional imperatives, we propose a concept for their semantic
representation and show that existing systems of monadic and dyadic deontic
logic can be reconstructed accordingly.
Notes to my DEON '00 contribution (postscript 240 kB, pdf 116 kB) Abstract: I take a closer look at the dyadic systems defined in my DEON '00 paper. In particular, the system DSDL3Minus is compared to systems P and R as used to describe nonmonotonic consequence relations.
Contribution to the DEON '02
workshop. Last revised 7th April 2003 for publication in the Journal
of Applied Logic, 2 (2004), 39-61.
Abstract: Deviating from standard possible
worlds semantics, authors belonging to what might be called the 'imperative
tradition' of deontic logic have proposed a semantics that directly represents
norms (or imperatives). The paper examines possible definitions of deontic
operators in such a semantics and some properties of according logical systems.
Contribution to the DEON
'04 workshop. Last revised 15th February 2005 for publication in the
Journal of Applied Logic 3 (2005), 484-511.
Abstract: Often a set of imperatives or
norms seems satisfiable from the outset, but conflicts arise when ways to
fulfill all are ruled out by unfortunate circumstances. Semantic methods
to handle normative conflicts were devised by B. van Fraassen and J. F.
Horty, but these are not sensitive to circumstances. The present paper extends
these resolution mechanisms to circumstantial inputs, defines dyadic deontic
operators accordingly, and provides a sound and (weakly) complete axiomatic
system for such deontic semantics.
Paper that
was presented to the working group "Law and Logic", XXII.
World Congress of Philosophy of Law and Social Philosophy (IVR 2005),
May 24-29th 2005, Granada, Spain. Accepted for publication in the Journal "Artificial Intelligence and Law". Last Revised November 23rd 2005.
Abstract: When
a conflict between duties is pointed out, often a resolution can be found
on the basis of an ordering between the apparently conflicting demands.
The paper examines how such a conflict resolution works, compares mechanisms
that have been proposed in the literature, and gives preference to one developed
by Brewka and Nebel. I provide accordingly defined dyadic deontic operators
and sound and complete axiomatic systems for two cases: that some conflicts
may remain unresolved, or a priority ordering can be determined that resolves
all.
Paper, accepted for publication in Theoria (submitted version, July 29th 2005).
Abstract: In a recent paper [Theoria 71 (2005) pp. 20-28], Sven Danielsson argued that the ‘original paradoxes’ of deontic logic, in particular Ross’s paradox and Prior’sparadox of derived obligation, can be solved by restricting the modal inheritance rule. I argue that this does not solve the paradoxes.
(To view postscript files, get the free programs Ghostscript and Ghostview here. To create postscript files, use a postscript printer driver, change properties to maximize portability, and print to file.)
3. I am currently combining the questions and results from my DEON 2000 - 2004 and IVR'05 papers into what hopefully will be my doctoral thesis. Though this is of course is my top priority right now, I am also planning more papers, so come back to this page soon.
4. If you're interested in online papers on Deontic Logic, consult the page of Leon van der Torre, where some great papers of his can be downloaded. Also try the author-links e.g. on the DEON '98 homepage, some have papers available (back to fish).
5. I had the pleasure of giving a seminar on deontic logic at the Institute for Logic, Leipzig University. For all of you interested, feel free to have a look at my lecture notes, put here as they progress (in German).
