Mapping agents

The agent on the basis of logical inference and the agent on the basis of the logical scheme are an expression of two opposite approaches to the design of agents: declarative and procedural. Their comparison can be carried out according to several parameters described below.

Brevity . An agent based on a logical scheme, unlike an agent based on an inference, is not required to have separate copies of its “knowledge” relating to each time interval. Instead, it refers only to data related to the current and previous time / x intervals. Both agents require copies of the “physical structure” descriptions (presented in the form of statements or logical schemes) for each square, and therefore they cannot adapt well to larger variations of the environment. In those variants of the environment, characterized by the presence of numerous objects, between which complex connections are established, the number of statements necessary exceeds the capabilities of any propositional agent. For such variants of the environment, the expressive power of first-order logic is required. In addition, propositional agents of both types are poorly adapted to represent or solve the problem of finding a path to the nearest safe square. (For this reason, the PL-Wumpus-Agent algorithm has to resort to using the search algorithm.)

Computational efficiency . In the worst case, logical inference may take time, depending exponentially on the number of characters, while calculating a logical value using a logic circuit takes time linearly dependent on the size of this circuit (or linearly dependent on the depth of this circuit if it is implemented as a physical device) . However, in practice (as shown above), the DPLL algorithm performs the required logic output very quickly.

Completeness . It was stated above that an agent based on a logical scheme may be incomplete due to limitations associated with acyclicity. But in fact, the reasons for incompleteness may be more fundamental. First of all, we recall that the duration of the task execution of the logic circuit linearly depends on the size of this circuit. This means that the logical scheme for some variants of the environment, which is complete (that is, allows us to calculate the truth value of any statement with a definable value), must be exponentially larger than the agent's knowledge base based on the logical inference. Otherwise, such a scheme would be an implementation of a certain way of solving the problem of finding a logical consequence in propositional logic in a time less than exponential, and this is highly unlikely. Another reason is the nature of the agent’s internal state. The agent on the basis of logical inference remembers the results of each perception and possesses knowledge, either explicit or implicit, about each statement that follows from these perceptions and initial knowledge base. For example, having received the result of perception B1; 1, this agent knows about the presence of a disjunction Р1 / 2 v р2 # 1, from which the statement B2l2- follows, based on a logical scheme, on the other hand, forgets all the results of perception obtained earlier and remembers only certain statements stored in registers. Therefore, the statements p1 # 2 and P2L, taken separately, become unknown to him after receiving the results of the first perception, i.e. he cannot conclude that the statement is true.

Ease of construction . This is a very important question that is not easy to find the exact answer. Of course, the authors of this book believe that it is much easier to formulate a statement about the "physical structure" declaratively, whereas the task of creating small, acyclic, not too incomplete logical schemes for the direct detection of wells seems very difficult for them.

Summing up, it can be concluded that in order to harmonize the requirements of computational efficiency, brevity, completeness and simplicity of design, it is necessary to come to certain compromises. If the relationship between perceptions and actions is simple (such as the relationship between Glitter and Grab), the logical solution can be considered the best solution, and a declarative approach may be the best for implementing more complex connections. For example, in a problem area such as chess, the declarative rules are short and simple to encode (at least in first order logic), and the logical scheme for calculating moves directly from the position data on the board would be unimaginably huge.

In the animal kingdom, it is often possible to detect various manifestations of such compromises. Lower animals with very simple nervous systems appear to be based on logical schemes, whereas higher animals, including humans, obviously have the ability to perform logical inference based on explicit concepts. This allows them to calculate much more complex agent functions. People also have logical schemes for the realization of reflexes, in addition, they may also have the ability to compile declarative representations for further use as logical circuits after some logical conclusions become routine. Thus, a hybrid agent project may have better abilities taken from both worlds.