Tag Archives: game

What are Quantifiers?

What are quantifiers?  Quantifiers have been thought of things that ‘range over’ a set of objects.  For example, if I say

There are people with blue eyes

this statement can be represented as (with the domain restricted to people):

∃x(Bx).

This statement says that there is at least one person with property B, blue eyes. So the ‘Ex’ is doing the work of looking at the people in the domain (all people) and picking out one with blue eyes.  Without this ‘∃x’ we would just have Bx, or x has blue eyes.

This concept of ‘ranging over’ and selecting an individual with a specific property out of the whole group works in the vast majority of applications.  However, I’ve pointed out a few instances in which it makes no sense to think of the domain as a predetermined group of objects, such as in natural language and relativistic situations.  In these cases the domain cannot be defined until something about the people involved are known, if at all; people may have a stock set of responses to questions but can also make new ones up.

So, since the problem resides with a static domain being linked to specific people, I suggest that we find a way to link quantifiers to those people.  This means that if two people are playing a logic game, each person will have their own quantifiers linked to their own domain.  The domains will be associated with the knowledge (or other relevant property) of the people playing the game.

We could index individual quantifiers to show which domain they belong to, but game theory has a mechanism for showing which player is making a move by using negation.  When a negation is reached in a logic game, it signals that it is the other player’s turn to make a move.  I suggest negation should also signal a change in domains, as to mirror the other player’s knowledge.

Using negation to switch the domain that the quantifiers reference is more realistic/ natural treatment of logic: when two people are playing a game, one may know certain things to exist that the other does not.  So using one domain is an unrealistic view of the world because it is only in special instances that two people believe the exact same objects to exist in the world.  Of course there needs to be much overlap for two people to be playing the same game, but having individual domains to represent individual intelligences makes for a more realistic model of reality.

Now that each player in a game has his or her own domain, what is the activity of the quantifier?  It still seems to be ranging over a domain, even if the domain is separate, so the problem raised above has not yet been dealt with.

Besides knowing different things, people think differently too.  The different ways people deal with situations can be described as unique strategies.  Between the strategies people have and their knowledge we have an approximate representation of a person playing a logic game.

If we now consider how quantifiers are used in logic games, whenever we encounter one we have to choose an element of the domain according to a strategy.  This strategy is a set of instructions that will yield a specified result and are separate from the domain. So quantifiers are calls to use a strategy as informed by your domain, your knowledge.  They do not ‘range over’ the domain; it is the strategies a person uses that take the domain and game (perhaps “game-state” is more accurate at this point) as inputs and returns an individual.

The main problem mentioned above can now be addressed: Instead of predetermining sets objects in domains, what we need to predetermine are the players in the game. The players may be defined by a domain of objects and strategies that will be used to play the game, but this only becomes relevant when a quantifier is reached in the game.  Specifying the players is sufficient because each brings his or her own domain and strategies to the game, so nothing is lost, and the domain and strategies do no have to be predefined because they are initially called upon within the game, not before.

I don’t expect this discussion to cause major revisions to the way people go about practicing logic, but I do hope that it provides a more natural way to think about what is going on when dealing with quantifiers and domains, especially when dealing with relativistic or natural language situations.

Posted in epistemology, game theory, logic, philosophy. Tagged with , , , , , , .

Video Game Design 2: Marionette Theater

Apropos my first post on video game design, I have thought up a new “game” for the Wii. It is a marionette theater simulator: you would get to create virtual marionettes, with customizable bodies and outfits (Mii integration if possible, lots of different clothing options), and levels would include performing different scenes from plays or entire plays. The accelerometers of the Wii controllers would function as the strings on the virtual marionettes. As you tilt the controllers different ‘strings’ would get pulled or slackened moving the different parts of the marionette’s body.

Interactive audio effects would be crucial: recorded voice acting for characters, dynamic background music and sound effects (e.g. when a marionette hits a wall, a thud could be made), with karaoke-style text of the characters’ lines scrolling across the screen, as an option (voice recognition, if possible). A scene/play creation mode would allow players access to creating their own sets, characters, and lines, giving the game infinite replay value (online sharing of new sets, characters, etc., and entire plays, if possible). Buttons could trigger effects on stage, change the motion control to different characters, have the marionettes pick objects up, change camera angle, etc.

If saving a marionette performance and text-to-voice is included (with user-defined manipulations – angry, soft, loud, etc.) a playwright could produce his or her play on the Wii and immediately distribute its virtual staging. This could be done by recording the output of the Wii, but if the Wii could upload and download complete performances, it would become an artistic platform.

A good puppet show is something amazing. Check out these scenes from Being John Malkovich done by Phil Huber:

Posted in design, fun, products, Wii. Tagged with , , , , , , .

Video Game design

I’ve bought meself a Wii and I quite like it. But there needs to be some more killer games.. freaking mercury meltdown got delayed. So for some reason – this is a first for me – I thought of a video game design. Simply put it is a spy game. The interesting thing is that each level is composed of 2 parts: the first part is a ‘training’ program put on by the spy agency to train the spy in what needs to be done. This ‘training program’ will not make use of the Wii motion sensors but will feature classic style gameplay only. Then the spy is sent on the mission but now to do everything will require using the motion controls. This game design will specific highlight the immersion that the motion controls bring to the game by contrasting them with the classic controls for doing the exact same operation. Also, the game design is efficient by reusing aspects of the same level design twice, though with different art direction, and differences in the ‘training’ and ‘mission’ – due to ‘incomplete intelligence’ – will make for good surprises. Ok game makers, hop to.

Posted in design, products, technology, Wii. Tagged with , , , , .