Modal logic: developments & applications in IT research areas

This post contains preliminary and very general research into recent developments in nonclassical (i.e. modal) logics and information technology and other relevant areas of study (namely, knowledge representation, computer programming, decision theory, artificial intelligence, verificationism)

A modal logic framework for multi-agent belief fusion

Liau, C. 2005. A modal logic framework for multi-agent belief fusion. ACM Trans. Comput. Logic 6, 1 (Jan. 2005), 124-174. DOI= http://doi.acm.org/10.1145/1042038.1042043

Keywords:
Epistemic logic, belief fusion, belief revision, database merging, multi-agent systems, multi-sources reasoning

ABSTRACT

This article provides a modal logic framework for reasoning about multi-agent belief and its fusion. We propose logics for reasoning about cautiously merged agent beliefs that have different degrees of reliability. These logics are obtained by combining the multi-agent epistemic logic and multi-source reasoning systems. The fusion is cautious in the sense that if an agent’s belief is in conflict with those of higher priorities, then his belief is completely discarded from the merged result. We consider two strategies for the cautious merging of beliefs. In the first, called level cutting fusion, if inconsistency occurs at some level, then all beliefs at the lower levels are discarded simultaneously. In the second, called level skipping fusion, only the level at which the inconsistency occurs is skipped. We present the formal semantics and axiomatic systems for these two strategies and discuss some applications of the proposed logical systems. We also develop a tableau proof system for the logics and prove the complexity result for the satisfiability and validity problems of these logics.

 

An internal semantics for modal logic

Fagin, R. and Vardi, M. Y. 1985. An internal semantics for modal logic. In Proceedings of the Seventeenth Annual ACM Symposium on theory of Computing (Providence, Rhode Island, United States, May 06 – 08, 1985). STOC ’85. ACM, New York, NY, 305-315. DOI= http://doi.acm.org/10.1145/22145.22179

ABSTRACT

In Kripke semantics for modal logic, “possible worlds” and the possibility relation are both primitive notions. This has both technical and conceptual shortcomings. From a technical point of view, the mathematics associated with Kripke semantics is often quite complicated. From a conceptual point of view, it is not clear how to use Kripke structures to model knowledge and belief, where one wants a clearer understanding of the notions that are primitive in Kripke semantics. We introduce modal structures as models for modal logic. We use the idea of possible worlds, but by directly describing the “internal semantics” of each possible world. It is much easier to study the standard logical questions, such as completeness, decidability, and compactness, using modal structures. Furthermore, modal structures offer a much more intuitive approach to modelling knowledge and belief.

First-order classical modal logic: applications in logics of knowledge and probability

Arló-Costa, H. and Pacuit, E. 2005. First-order classical modal logic: applications in logics of knowledge and probability. In Proceedings of the 10th Conference on theoretical Aspects of Rationality and Knowledge (Singapore, June 10 – 12, 2005). R. van der Meyden, Ed. Theoretical Aspects Of Rationality And Knowledge. National University of Singapore, Singapore, 262-278.

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like FOL + K) in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. We conclude by offering a general completeness result for the entire family of first order classical modal logics (encompassing both normal and non-normal systems).

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Online Research in Philosophy (sponsored by David Chalmers)

David Chalmers, a contemporary analytic philosopher specializing in consciousness and possible world semantics, has embarked on another online philosophy service: online research in philosophy.

I’ll post a review of it after I have been able to spend sufficient time with it. Needless to say at first glance I am impressed. Anyone interested in academic philosophy should create a free profile.

Mine is available at http://philpapers.org/profile/6668

Commentary on Wittgenstein’s Brown Book (pg 171, comment #19)

Wittgenstein discusses the deceptive way in which philosophy attempts to resolve the “peculiar” way in which names designate objects.

When we think of a method of designation as the correlating of an utterance and a particular thing (or object), the use or function of the utterance is no longer a primary concern for us.  Thus for Wittgenstein’s sense of meaning as use, we lose the meaning of what we utter.

Explanatory philosophy ends up reducing or constricting the use of an expression to a non-contextual, purely grammatical, mysterious relation. The substitution terms end up forming the relation itself. One that can be applied in a number of cases, but only at the expenses of a more grounded and useful description.

Take away the reason for a particular term to belong to the category “mental events” or “intentionality” and you take away the seemingly inherent mystery or intrigue that blinded you to the term’s original use (i.e. real meaning).

Here’s Wittgenstein’s comment, with the comments above as linked footnotes so you can see what I am exactly responding to:

#19.  The danger of delusion which we are in becomes most clear if we propose to ourselves to give the aspects ‘this’ and ‘that’ names, say A and B. For we are tempted to imagine that giving a name consists in correlating in a peculiar and rather mysterious way a sound (or other sign) with something. How we can make use of this peculiar correlation then seems to be almost a secondary matter. (One could almost imagine that naming was done by a peculiar sacramental act, and that this produced some magic relation between the name and the thing.)[DP1]

But let us look at an example; consider this language game: A sends B to various houses in their town to fetch goods of various sorts from various people.  A gives B various lists.  On top of every list he puts a scribble, and B is trained to go to that house on the door of which he finds the same scribble, this is the name of the house.  In the first column of every list he then finds one or more scribbles which he has been taught to read out.  When he enters the house he calls out these words, and every inhabitant of the house has been trained to run up to him when a certain one of these sounds is called out, these sounds are the names of the people. He then addresses himself to each one of them in turn and shows to each two consecutive scribbles which stand on the list against his name. The first of these two, people of that town have been trained to associate with some particular kind of object, say, apples.  The second is one of a series of scribbles which each man carries about him on a slip of paper.  The person thus addressed fetches say, five apples.  The first scribble was the generic name of the objects required, the second, the name of their number.

What now is the relation between a name and the object named, say, the house and its name? I suppose we could give either of two answers. The one is that the relation consists in certain strokes having been painted on the door of the house.  The second answer I meant is that the relation we are now concerned with is established, not just by painting these strokes on the door, but by the particular role which they play in the practice of our language as we have been sketching it.-Again, the relation of the name of a person to the person here consists in the person having been trained to run up to someone who calls out the name; or again, we might say that it consists in this and the whole of the usage of the name in the language game.

Look into this language game and see if you can find the mysterious relation of the object and its name.-The relation of name and object we may say, consists in a scribble being written on an object (or some other such very trivial relation), and that’s all there is to it. But we are not satisfied with that, for we feel that a scribble written on an object in itself is of no importance to us, and interests us in no way. And this is true; the whole importance lies in the particular use we make of the scribble written on the object, and we, in a sense, simplify matters by saying that the name has a peculiar relation to its object, a relation other than that say, of being written on the object, or of being spoken by a person pointing to an object with his finger. A primitive philosophy condenses the whole usage of the name into the idea of a relation which thereby becomes a mysterious relation.[DP2] (Compare the ideas of mental activities, wishing, believing, thinking, etc., which for the same reason have something mysterious and inexplicable about them.)[DP3]


[DP1]When we think of a method of designation as the correlating of an utterance and a particular thing (or object), the use or function of the utterance is no longer a primary concern for us.  Thus for Wittgenstein’s sense of meaning as use, we lose the meaning of what we utter.

[DP2]Explanatory philosophy ends up reducing or constricting the use of an expression to a non-contextual, purely grammatical, mysterious relation. The substitution terms end up forming the relation itself. One that can be applied in a number of cases, but only at the expenses of a more grounded and useful description.

[DP3]Take away the reason for a particular term to belong to the category “mental events” or “intentionality” and you take away the seemingly inherent mystery or intrigue that blinded you to the term’s original use (i.e. real meaning).

E-Marketing’s challenges

According to one study (Manisto, 1999) participants in an e-marketing questionaire indicated privacy concerns and censorship as the two top issues that were hindering the growth of e-commerce.  In developing countries, respondents painted a much different picture.  Respondents in emerging countries listed the following as major obstacles:

  • insufficient local content
  • costs associated with domestic plans
  • ISP-associated performance and costs
  • lack of content in native language

Strauss, El-Ansary, and Frost correctly implicate the additional cost of insecure online transactions as well as fradulent and/or malicious credit card users.

philosophy vs. information technology – printing requirements

I’m not a fan of discussing something in the context of that thing’s nature.  Thus I dislike saying things like: “well the nature of Wittgenstein’s philosophy is such that…”  Use of the expression imitates that conception of natural and/or logical necessity that Wittgenstein’s later developments (language games, the concept of grammar) nicely opposed, if not the necessity per se, its ill philosophical effects.

This is going to seem irrelevant but and it sort of is, but we could introduce another sort of language game where I’m apt to use or convey that sense of necessity I just got through justifying a disagreement with.  This has more practical relevance – printing requirements.  I figured my undergraduate stint with philosophy would, naturally, of necessity (yes I’m stretching it) – represent more in terms of printing costs vs. my graduate studies information technology.  After all, those old philosophy research papers from the 1940s, they’re available in PDF, but nobody would think (I hope not) to try to read them on a monitor where resolutions are roughly (something like) 40% that of the resolution of the real deal (i.e., reading a real book).  And since IT itself is a new discipline, it stands to reason that documentation ought to be primarily available on screen, right?

None of this turns out, with me, to be true.  I’m beginning to mooch off the network printers and/or printers of my family/peers.  So yeah, this is all leading up to my find for the week.  Practical knowledge is the new metaphysical necessity, it helps to not purchase your printing equipment at oversized vendors with terrible prices.  So yeah, this is definitely a practical post.

Printing needs

IT security surveys typically run anywhere from 20-50+ pages with lots of images and/or non-text/colored content.  Lexmark printers – especially the inkjets –  are pretty good for undergraduate/mid-level printing requirements.  I bought the Z1300 a year or so ago and while basic, its completely fine for low to mid-level use.  My gripe has to do with the software, and an aspect of it that’s quite irrelevant to its functionality.  There’s this annoying voice that activates whenever you use the thing, so I recommend NOT wearing headphones if you’re about to print something.  Of course you could shut it off in the options but who remembers that?  I’ll have to dig up an article on CNET which – I recall – named the z1300 a definite grab for the price.  If I buy online I tend to gravitate towards vendors who’ve been around for awhile and that sport high customer ratings.

Anyway, for printer toners and ink/other printer supplies its probably easiest to buy the stuff online. Make sure to review CNET or Tom’s Hardware Guide or something to make sure the stuff you purchase is legitimate and/or corresponds with your printer.  Might pay a few extra bucks for shipping but from what I can tell the price is initially reduced at the best online vendors.  If the vendor’s been around for several years chances are you should feel confident buying printing supplies from them.

Scanners

Scanners probably aren’t too necessary for most undergraduates unless they’re into photo editing and/or really wanna share old pictures on social networking sites.  Color depth is important to watch out for, although honestly I dont’ know much about scanners other than a few good shopping places online.

Although, scanners would be extremely useful if you’re considering going into digital/online publishing for instance.  Especially if you were an editor or content producer for an academic publication, since physical documents are still digitally scanned as part of the update process for large academic databases such as EBSCO.

The Duty of Genius

“We say that someone has the eye of a painter or the ear of a musician but anyone lacking these qualities hardly suffers from a kind of blindness or deafness.”

“We say that someone doesn’t have a musical ear, and aspect-blindness is (in a way) comparable to this inability to hear.”

These are quoted from Ray Monk’s great biography of Wittgenstein, The Duty of Genius. Apparently Wittgenstein uttered them in conversation with his friend, Drury, a psychologist.

a new appreciation for modal logic

As I venture deeper into my studies, I’m beginning to reaffirm my confidence in modal logic.  This is primarily a function of seeing how it can be used at an applied/industrial level.  I’m only beginning to understand, or in some cases, conjure, ways in which a logical model of a database, for instance, might be describable in modal propositional logic.  Since I haven’t been able to achieve this at a sufficient level, I’ll hold off on sharing my exact thoughts.  Needless to say, even this Stanford Encyclopedia of Philosophy entry on modal logic characterizes some of its commercial and/or industrial application.

The applications of modal logic to mathematics and computer science have become increasingly important. Provability logic is only one example of this trend. The term “advanced modal logic” refers to a tradition in modal logic research that is particularly well represented in departments of mathematics and computer science. This tradition has been woven into the history of modal logic right from its beginnings (Goldblatt, 2006). Research into relationships with topology and algebras represents some of the very first technical work on modal logic. However the term ‘advanced modal logic’ generally refers to a second wave of work done since the mid 1970s. Some example of the many interesting topics dealt with include results on decidability (whether it is possible to compute whether a formula of a given modal logic is a theorem) and complexity (the costs in time and memory needed to compute such facts about modal logics).

My recent attempt involved attempting to translate simple E-R logical data flows into modal propositions, though without quantification it was difficult and/or probably impossible.