# Catalogue of Artificial Intelligence Techniques

## Temporal Logic

**Keywords:**
Event
Calculus, modal temporal logic

### Categories: Inference and Reasoning , Knowledge Representation , Planning

Author(s): **Han Reichgelt**

Temporal logic deals with reasoning about time. There are three
different approaches to temporal logic. The first approach is the
Situation Calculus. In the situation calculus,
one simply adds an argument to each predicate which represents the
time at which the predicate is assumed to be true. Thus, a two-place
predicate like `hit' becomes a three-place predicate, and the
proposition that `Harry loves Mary at time t' is represented simply as
`hit(harry,mary,t)`

. The second approach is the reified approach.
In the reified approach, of which the Event Calculus is an example, one complicates the language by introducing
separate terms for events, processes etc. as well as a predicate
which is sometimes called `HOLDS`, sometimes `TT`, for saying
that an event took place at some time. So, to express the proposition
that `Harry hit Mary at time t,' one would write
`HOLDS(hit(harry,mary),t)`

, where `hit(harry,mary)`

is a functional
expression denoting the event of `Harry hitting Mary.' The final and
third approach, which has not been too popular in AI, is
modal temporal logic. One introduces a
number of modal operators (see Modal Logic),
such as `P` (for past) and `F` (for future) and uses these to
represent time-dependent information. For example, the information
that `Harry hit Mary in the past' is represented as
`P(hit(harry,mary))`

.
Reasoning about time is important in a number of areas in AI. In
planning, for example, it is necessary to reason about the effects that an
action will have on the world, and this involves reasoning about
future states of affairs. Another example is natural language
processing where one is concerned with extracting temporal information
from the tenses of sentences.

### References:

- Turner, R.,
*Logics for Artificial Intelligence*, Wiley, New York, 1984.

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