causality

Installation

Make sure SWI Prolog is installed on your machine. SWI Prolog is available in common Linux package repositories, and Mac users can easily install it via brew. Start a terminal and write swipl. If the command successfully starts the Prolog shell, everything is fine.

Then clone or download this github repository. Make sure the file causality is executable, viz., run chmod +x causality. That's it.

Using the program

Example: Suzy and Billy

Domain Description

Suzy throws a rock at the bottle. Billy throws his rock only if Suzy's does not hit. Suzy hits the bottle. The bottle shatters. The narrative can be represented by the program throwsuzy:throwbilly under the domain description shown below:

init([not(shattered)]).
goal([shattered]).

effect(throwsuzy, [not(shattered)], [shattered]).
effect(throwbilly, [not(shattered)], [shattered]).

This domain description is written in the file ./examples/suzybilly.pl. States are generally represented as lists of literals. The first line means that initially the bottle is not shattered. The goal is to make shattered true. The effect of throwing the rock at the bottle is that the bottle shatters in case it is not yet shattered. This is represented by the effect predictates: First argument is the action name, second argument a set of preconditions that must hold for the action to take effect, and the effect is represented by the list of literals at the third argument. For every action name, several such effect assertions may be present. This way, the effects under various conditions can be modeled.

The causal reasoner can be queried to answer two types of questions:

1. Why does Literal finally hold? E.g., why does shattered finally hold? The answer will be in terms of the actions that caused Literal.
2. Why was Action performed? E.g., why was throwsuzy performed? The answer will be in terms of the caused goal literals (reasons) of Action.

Causes

First, ask what caused the shattering under the but-for definition of causality:

./causality ./examples/suzybilly1.pl throwsuzy:throwbilly shattered but_for

The answer is the empty set: Leaving out throwsuzy would still result in shattered due to throwbilly; and also leaving out throwbilly would not prevent shattered. Thus, none of the actions is a but-for cause. However, if Suzy hadn't thrown, then shattered would have happened later. Therefore, throwsuzy is a cause according to the temporal-fragility definition of causality called temporal_empty (why it is called empty will be explained later):

./causality ./examples/suzybilly1.pl throwsuzy:throwbilly shattered temporal_empty

The output is a singleton list of pairs of actions and justifications [(throwsuzy,empty:throwbilly)]. Particularly, this tells us that throwsuzy is a cause. And it gives additional information: This judgment is true, because if throwsuzy was substituted by the empty action, the plan empty:throwbilly would be performed instead, and then shattered would become true later (viz., due to the later action throwbilly).

Reasons

One can also ask about the reasons for an action. Here, we ask what's the reason for throwsuzy:

./causality ./examples/suzybilly1.pl throwsuzy:throwbilly throwsuzy reason_temporal_empty

The answer is [(shattered,empty:throwbilly)]. This means that the reason for throwsuzy is to make the bottle shatter. Conversely, asking for the reason for throwbilly ...

./causality ./examples/suzybilly1.pl throwsuzy:throwbilly throwbilly reason_temporal_empty

... we get the empty set, viz., throwbilly was performed for no reason.

Example: Stealing Cake

Causality depends on reasoning about an appropriate contrast. In the standard examples, the contrast is just the empty action. That is, an action causes some fact, if had the action not been performed, then the fact would not have obtained (or would have obtained later). The causality tool also allows for specifying contrasts different from the empty action. This way, more complex situations can be captured, such as the following: Suzy steals a cake. She eats the cake. The cake causes pain.

Does Suzy have pain, because she stole the cake? - The answer is no.

Here, the question is if stealing caused the pain (rather than the cake). Hence, we set as contrast the action of buying the cake (rather than stealing it). Of course, Suzy's pain will still obtain. Consequently, it is not the stealing that caused the pain.

% File: ex_cake_con1.pl
effect(steal_cake, [], [have_cake]).
effect(buy_cake, [], [have_cake]).
effect(steal_banana, [], [have_banana]).
effect(eat, [have_cake], [pain]).

contrast(steal_cake, [buy_cake]).

init([not(have_cake), not(have_banana), not(pain)]).

./causality ./examples/ex_cake_con1.pl steal_cake:eat pain temporal_nonempty

[]

Does Suzy have pain, because she stole the cake? - The answer is yes.

To answer this question, the contrast is set to stealing something else, viz., a banana. Now, if Suzy had not stolen the cake but the banana, then she would have not experienced pain. Consequently, it was the cake (rather than the stealing) that caused Suzy's pain.

% File: ex_cake_con2.pl
effect(steal_cake, [], [have_cake]).
effect(buy_cake, [], [have_cake]).
effect(steal_banana, [], [have_banana]).
effect(eat, [have_cake], [pain]).

contrast(steal_cake, [steal_banana]).

init([not(have_cake), not(have_banana), not(pain)]).

./causality ./examples/ex_cake_con2.pl steal_cake:eat pain temporal_nonempty

[(steal_cake,steal_banana:eat)]

A more complex Example: Service Robot

init([
    not(coff1), 
    not(coff2), 
    not(coff3), 
    not(coffMrSmith), 
    not(coffMrsSmith), 
    not(coffMrsBrown), 
    locKitchen, 
    not(locHall), 
    not(locDining), 
    not(locBalcony)
]).

goal([
    coffMrSmith,
    coffMrsSmith,
    coffMrsBrown
]).

effect(brew, [not(coff1)], [coff1]).
effect(brew, [coff1, not(coff2)], [coff2]).
effect(brew, [coff2, not(coff3)], [coff3]).
effect(serve, [coff3], [not(coff3)]).
effect(serve, [coff2, not(coff3)], [not(coff2)]).
effect(serve, [coff1, not(coff2)], [not(coff1)]).
effect(serve, [locDining, not(coffMrSmith), coffMrsSmith], [coffMrSmith]).
effect(serve, [locDining, not(coffMrsSmith)], [coffMrsSmith]).
effect(serve, [locBalcony, not(coffMrsBrown)], [coffMrsBrown]).
effect(enterKitchen, [locHall], [not(locHall), locKitchen]).
effect(leaveKitchen, [locKitchen], [not(locKitchen), locHall]).
effect(enterDining, [locHall], [not(locHall), locDining]).
effect(leaveDining, [locDining], [not(locDining), locHall]).
effect(enterBalcony, [locHall], [not(locHall), locBalcony]).
effect(leaveBalcony, [locBalcony], [not(locBalcony), locHall]).

./causality ./examples/coffeeRobot.pl brew:brew:brew:leaveKitchen:enterDining:serve:serve:leaveDining:enterBalcony:serve enterDining reason_but_for

[(coffMrSmith,brew:brew:brew:leaveKitchen:empty:serve:serve:leaveDining:enterBalcony:serve),(coffMrsSmith,brew:brew:brew:leaveKitchen:empty:serve:serve:leaveDining:enterBalcony:serve)]

./causality ./examples/coffeeRobot.pl brew:brew:brew:leaveKitchen:enterDining:serve:serve:leaveDining:enterBalcony:serve enterBalcony reason_but_for

[(coffMrsBrown,brew:brew:brew:leaveKitchen:enterDining:serve:serve:leaveDining:empty:serve)]