jump to navigation

A Math of Morality and Belief March 4, 2013

Posted by ficial in brain dump.
Tags: , , , , ,
trackback

Our kid is now a bit over 2 years old, which means he’s well into the sociopathic midget stage of growing up, and I’ve just been reading a future-of-humanity novel (Accelerando, by Charles Stross – I give it 3.5 out of 5; it’s flawed, but has some interesting ideas anyway. For a better version of more-or-less the same kind of thing I’d recommend Schismatrix by Bruce Sterling instead). So, that’s gotten thinking about building/creating/evolving and describing morality systems. We can’t expect anything – a child, a corporation, a program – to behave morally unless that thing has a way to represent what it means to be moral. For people we pretty much just wing it and they pretty much learn it (where ‘it’ is ‘some way to evaluate actions and the world’ rather than any particular moral/belief structure) as they grow up. For other things… well, we shouldn’t expect a strong AI to be moral if it’s source doesn’t contain a way for it to have and evolve a moral system. So, between all that and the mild fever from the tail end of a cold, I give you my first stab at:

A Math of Morality and Belief

Part 1: Establishing a formal framework / terminology for discussion and analysis of morality and belief structures. This framework should handle everything from people to business to software to trees.

DEF: “trait”: an arbitrary element (a scalar)
DEF: “value”: an arbitrary element (a scalar, or possibly a complex structure)
DEF: “trait-value”: a set {t,v} where t is a trait and v is a value

DEF: “world state”: a set of trait values where no trait is in more than one trait-value.
NOTE: a trait t1 in a world state c may be referred to as c.t1. The value v1 of a trait-value {t1,v1} in the world state c may be referred to as c.t1.v1
NOTE: a world states are of necessity limited approximations / representations of the whole, real universe.
DEF: “dense world state”: a world state that has relatively many traits and attempts a relatively accurate representation of the real universe
DEF: “sparse world state”: a world state that has relatively few traits and represents a relatively limited and/or abstract representation of the real universe

DEF: “an action”: an action is a function on a world state that results in another world state
DEF: “valid action”: an action is valid for a world state c when
* action(c) = cprime
* there exists at least one trait tx such that cprime.tx.value != c.tx.value
NOTE: under this formal definition of “action” the human language concept of “take no action” would be an action if it resulted in a changed world state.

DEF: “action value”: a set containing an action and a number from 0 to 1
DEF: “action space”: a set action values, where no action appears in more than 1 value

DEF: “imperative”: a function that takes an any action and returns a number from 0 to 1, or a null (which means “this imperative does not apply”)
DEF: “evaluative”: a function that takes any world state and returns a number from 0 to 1, or a null (which means “this evaluative does not apply”)
DEF: “a belief”: shorthand for “an imperative or an evaluative”
DEF: “situational relevance”: a function that takes a world state and a belief and returns a number from 0 to 1
NOTE: these kind of functions need to be able to handle ANY world state or action, and thus must be implemented as a finite system with a default handler for anything the system doesn’t know how to evaluate (typically, the default is ‘null’, though it could also be a number generated with some kind of parameterized randomizer). The system which these functions use can process individual traits and values, and can also handle the world state as a whole (e.g. look at the count of trait-values).
NOTE: the situational relevant function may NOT return a null – it’s implementation must always return a number between 0 and 1.

DEF: “means-ends balance”: a function that takes two numbers each from 0 to 1, the first number representing a valuation of a means and the second of an end, and returns a number from 0 to 1

DEF: “bounds”: a function that takes a number from 0 to 1 and returns true or false
DEF: “out of bounds”: a number for which the bounds function returns false

DEF: “belief system”: a set containing 0 or more beliefs, a situational relevance, a means-end balance, and a bounds
NOTE: belief systems may be complex, but they can also be very basic – e.g. a tree could have a very simple ‘belief system’ that contains no imperative, a few very straightforward evaluatives, and blind functions for situational relevance, means-end balance, and bounds.

DEF: “viable context (of a belief system)”: the set of all world states and actions for which at least one belief in the system returns a number (i.e. not null).

DEF: “entity”: a set of trait-values and a belief system
NOTE: entities may be values of a world state

DEF: “possibility”: a world state and a set of 1 or more actions that are valid for that world state

DEF: “capability”: an entity and a possibility; the entity is one of the values of the world state of the possibility

DEF: “agent entity”: the entity in a capability

DEF: “non-agent entity”: an entity in a world state of a possibility for which there does not exist a capability containing that entity and that world state

DEF: “judgement”: a function that takes a capability (or an entity and a possibility) and an action in that capability(or possibility) and returns a number from 0 to 1, or null (meaning the action is irrelevant to the agent or entity) that is generated by running the agent’s (or entity’s) world state-weighted (via situational relevance) beliefs against the action and the hypothetical result-world state of that action.

DEF: “action judgements”: the action space that is generated by judging each action in a capability

DEF: “allowable actions”: the action space that is generated by judging each action in a capability and excluding any for which the result is out of bounds

DEF: “acceptable action”: a function that takes an entity, a possibility, and an action in that possibility and returns a true or false. The response is true if the action is in the allowable actions set for that entity and possibility, or if the judgement of the action is null. The response is otherwise false.

DEF: “morally relevant to an entity”: a world state is morally relevant if there exists a capability that contains that entity and that world state, and at least one action in the capability is not in the allowable actions of that capability

DEF:”morality space of an entity”: the set of all world states that are morally relevant to an entity
DEF:”morality space of a belief system”: the set of all world states that are morally relevant to an entity that holds the belief system

DEF: “impacted entity”: an an entity in a world state in a possibility for which the action judgements contain at least one non-null value.

DEF: “solipsistically optimal action”: the highest rated action in allowable actions

DEF: “tolerance”: tolerance is one of the traits for an entity (or possibly an addition to a belief system – the distinction gets a bit blurry; perhaps the elements of a belief set are flattened into attributes of an entity). Its value is a number from 0 to 1. Tolerance becomes relevant when the world state of an agent’s capability includes 1 or more other entities. It measures how far below the solipsistically optimal action value the agent is willing to go to select an action that is acceptable to the other entities.
NOTE: the method/function which an agent uses to composite ratings of other entities could also be a trait value of the entity or another element of a belief system.

DEF: “tolerable actions”: all actions with a rating within tolerance of the solipsistically optimal action

DEF: “tolerantly optimal action”: the highest rated action with a rating within tolerance of the solipsistically optimal action for which that action is acceptable to the other entities in the world state (or a maximal subset of them).

DEF: “empathy “: empathy is another trait for an entity. Its value is a number from 0 to 1. It indicates how far below the tolerantly optimal action the agent is willing to go in order to maximize the composite of the judgements of the other entities.

DEF: “empathetically optimal action”: the action within the empathy range of the tolerantly optimal action for which the composite of ratings of other entities for that action is highest.

 

Part 2: Exploration of entities and morality. Currently unwritten. I may get to it someday, or I may not. I would enjoy discussing this topic with anyone interested.

Comments»

No comments yet — be the first.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

%d bloggers like this: