Belief Review: What It Is, Types, And How It Works
Suppose we have a database or computer program that contains, among other information, the following data encoded in some logical way:
If our program is capable of making logical inferences, the result of the operation of the four pieces of information will be the coyote is gray. However, let’s assume that this is not true and the coyote has yellow fur. So, we should deny the information that the coyote found is white and add it to the database, but then we create an inconsistency with the rest of the stored information.
To maintain the reliability of the data, it would be necessary to review the previously stored data and rectify any of the beliefs established before the new event. For this, it is not necessary to renounce all the previous premises, since this would mean an unnecessary and important loss of information. So you have to choose one.
The problem of the revision of beliefs It refers to the fact that logical information alone does not indicate which of them must be renounced, but rather that other means must be used to elucidate which ones to remove or modify. Furthermore, any choice will have logical consequences when making new inferences, so when abandoning a belief we must also decide which consequences we want to keep and which are obsolete.
Efforts to create logical agents that act rationally ultimately involve formalizing the process of belief revision. This implies take new information into account and adjust one’s belief state, or epistemic state, accordingly
There are multiple ways to modify a belief state when new information is obtained. For example, consider an agent who believes that “Paul is a priest” and “priests are not married.” If this agent learns that Pablo got married, the belief state becomes inconsistent and one of the statements must be discarded to resolve the inconsistency.
Belief revision, or belief change, refers to the act of changing or adding new beliefs When adding a disagreeing belief, the contradictory beliefs must be removed or modified so that they remain consistent. This is possible because beliefs are represented by a set of sentences that can be deleted or introduced, requiring consistency adjustments with the other stored sentences.
Changing beliefs requires compliance with specific rationality guidelines. These rules have been proven through representation theorems derived from postulates related to specific operations involving beliefs and their representations.
1. Review and update of information.
There are two main types of changes, which are usually divided into more specific changes.
1.1. Update
Updating beliefs means adjust them to reflect new information This involves changing old beliefs for new ones, which refer to the current situation.
1.2. Revision
New information may be inconsistent with old beliefs Old beliefs are likely to be less reliable than new ones. In this case, new information can create an inconsistency. This conflict-avoiding process is called revision, which is when new information is inserted into a set of old beliefs, without incompatibility occurring.
To minimize the impact of the belief revision process, knowledge should remain as similar before and after a revision or update This principle is known as least change, which formalizes the assumption that people are unlikely to change their minds. It also mandates that when updating beliefs, one must preserve as much prior knowledge as possible.
The following classic example shows that the operations required to update and revise beliefs are not the same. It is based on two different perspectives regarding new information:
Two satellites, A and B, are orbiting Mars with the mission of landing. These emit a continuous signal about their location to the base. The earth receives a signal that one of the two satellites is still in orbit; However, due to a technical problem, it does not know which satellite has broadcast the data. A while later, the signal is received that satellite A has landed on Mars. According to the data update operation, the information of satellite A is adjusted and the position of B is unknown (which is not updated). A does not interfere with B, which we do not know if it has landed or is still in orbit.
In the review example, let’s say that a city has two theaters, and play A will be performed in one of the two. This is the first information we can save. Next, we know that on the same dates a play B will be performed in the first theater. In this case we can infer that play A will be performed in the theater that remains free. There is a revision operation, when introducing new information.
2. Other operations
In a certain situation where all the beliefs involved refer to the same scenario additional operations can be performed including:
Contraction: the elimination of a belief.
Expansion: adding a belief without checking consistency
Extraction: elimination of a consistent set of beliefs
Consolidation: reestablishing the coherence of a set.
Fusion: combining two or more belief systems into one, maintaining consistency. However, this differs from the review in that it does not prioritize new data.
Development of research on belief revision
Since the mid-1980s, belief revision has been considered its own topic. This term was created from two related fields of research: computer science and philosophy
Since the beginning of computer science, programmers have created different procedures to update databases. With the development of Artificial Intelligence, increasingly complex database update models have been proposed. In 1979, truth maintenance systems came to light; capable of revising their beliefs to maintain consistency with new information that contradicts existing information. In 1983, one of the most important theoretical contributions to the revision of beliefs arrived, the notion of priority was introduced Prioritization uses predefined rules to determine which data source takes priority over other data sources when updating.
Since ancient times, changing beliefs has been the subject of philosophical reflection. Already, in the 20th century, there were more specific debates focused on changing beliefs. These discussions involve judging whether changes in probability were rational and determining the mechanisms used to develop scientific theories. Later, in the 1970s, debates occurred focusing on the requirements for rational belief changes. Philosopher Issac Levi addressed many concerns in the field of linguistic research and belief revision in the 1970s.
In 1985, Carlos Alchourrón, Peter Gärdenfors, and David Makinson wrote an article that provided a formal framework for studies of belief change. Since then, The AGM model has been used to organize new knowledge related to belief changes this being the theoretical core.
Related article: “History of Psychology: authors and main theories”
The AGM model
The AGM model is the most commonly accepted theory of belief revision. Establishes that beliefs are represented by a logically closed set of sentences It should be noted that both in the AGM model and in most belief revision models, beliefs are represented by sentences written in some formal language. The phrases are not capable of capturing all the nuances and aspects of the belief, but they are currently considered the best representation of a general nature.
The set of beliefs is capable of expansion, contraction and revision Expansion occurs when a new proposition is added to the set, which is then logically closed. In contraction one of the propositions in the set is eliminated, closing again logically. Finally, revision refers, like expansion, to adding a new proposition to the set, but it must continue to be consistent.
The expansion operation is simple; reduction and revision operations can be multiple. The authors only discuss multiple possible operations that must obey certain postulates of rationality. Shrinkage operations require:
Closing
Success
Inclusion
Recovery
Emptiness
Extensionality
One of the most discussed topics in belief revision theory is the recovery postulate. This states that if a belief is deleted and then reinserted, all the original beliefs will be recovered. However, this does not apply to belief bases, which are similar models that use logically closed sets of beliefs There has been much discussion about how the AGM model represents changes in beliefs. Several alternative models have been proposed that purport to provide a more realistic explanation of belief changes than the AGM model.
