The urban planning is required to direct the cities development based on the sustainable use of its territory. On the other hand, Answer Set Programming (ASP) is a logic programming paradigm with the ability of non-monotonic reasoning, which has contributed to solving complex problems in a short period of time, providing a considerable number of possible outcomes to the same problem. The treatment of sustainable urban planning by using a declarative approach like ASP has not been proposed so far. This article aims to demonstrate a modelling exercise using basic knowledge about a mix of urban land usage. Also, to show alternatives for a better functional integration of green and habitational areas, as well as a discussion of further research using this approach.
The need to think about an ordered cities growth and their development, are
not new topics. The proposal on strategic measurements to improve the
conditions of cities, is one of the issues considered in the Agenda 21, to promote the
construction of an international sustainable model for the twenty- rst century
[
Derived from the above, with support from the United Nations Environment
Programme (UNEP), di erent countries worldwide have joined forces in order
to adapt environmental policies into their development processes with a
sustainable approach. The Institute of Hygiene, Epidemiology and Microbiology of the
Ministry of Public Health of Cuba in coordination with the World Health
Organization (WHO) and UNEP through the Latin American and the Caribbean
Regional O ce, have proposed a classi cation of six universal principles for
planning a sustainable urban ecosystem [
Taking into consideration the principles 2,3 and 6, this article proposes forming a basic knowledge that serves an intelligent system in resolving a complex combinatorial problem such as urban land use planning. Initially this article mentions works that use Knowledge Representation (KR) as a support in the eld of organization of urban territories, then the land use term is de ned as part of sustainable urban planning and an introduction to ASP is provided. Consecutively both issues are linked to generate a proposal where ASP contributes to the de nition of urban land use. This paper concludes with a discussion of the preliminary results and future work. 2
Land use and urban planning in general have been areas of interest to the scienti c community. Reason why, they have developed works that employ technology as a way to propose alternatives for cities improvement. For purposes of this paper, the works mentioned below have used some method of KR.
One of the rst works is the URBYS system, de ned as an expert system for
urban areas analysis through KR for decision-making [
Changing the subject, ontologies is another used and proven approach in
works like OSMoSys [
It should be noted that these examples have used di erent approaches of AI to resolve urban problematics. Nevertheless, so far none has taken advantage of the bene ts of ASP to solve these problems and that is why the strategy proposed in this article is unique in its class. 3
A standard de nition of land use is the employment that humans make the earth's surface, covering the management and modi cation of the natural environment to make it a built environment3. Examples are human settlements that 3 https://en.wikipedia.org/wiki/Land use involve industrial parks, shopping centers, roads, green and residential areas, among others.
Within the universal principles for sustainable urban ecosystem planning
previously mentioned, three of them are directly linked to land use planning
purposes considering the functional integration between green and residential
use areas [
This work considers the functional integration of green and residential areas as part of land use planning in a city. Reasons why the principles, protected vegetation, soil quality and human scale urban environment are interrelated. The fact that exists areas with trees, keep soil and air quality and this kind of conditions are attractive for living. These three principles handle certain rules, restrictions, conventions or preferences that allow forming a knowledge base for modeling desirable behavior in order to adapt to conventional urban spaces. 4
Several researchers have proposed the use of ASP as a solution to the paradigm
of Knowledge Representation and Reasoning (KRR) [
ASP has been tested successfully in areas, which involve problems of
combinatorial search using a considerable amount of information to process [
Additionally, ASP is based on a simple yet expressive rule language that
allows users to easily model problems in a compact form. The solutions to such
problem are known as answer sets or stable models [
Problem Representation in Logic Form To properly represent a problem it is necessary to segment it into three logical components: Facts and Constraints, Preferences and Real Scenarios or Input: Facts and Constraints: are those foundations that we can get from a speci c problem whether they are not going to change or are prohibited. In other words are the guidelines and parameters involving sustainable urban planning.
Preferences: Establish rules and restrictions about situations preferable over
others [
Modeling rules, constraints and preferences give us the parameters of what is desirable, undesirable and preferably having and not having to solve a problem based on the input. This information will be extracted from literature and real sustainable cases (RSC) to become KB (Fig1). The Real Scenario or Inputs: refers to the current situation once modeled the problem. This needs to include a well-detailed description or speci c characteristics of a determined urban center. This set will call R (Fig2).
If R changes, the result will be di erent even if KB does not change. The bene ts of ASP allow us depending on the complexity of the problem, is possible to have a wide range of perspectives for decision-making from the same R.
Once represented a complex problem as speci ed in the preceding paragraphs, it is necessary to translate this information into logical language for ASP. Taking as example urban land usage, there may be more than 3 or 4 ways to grow a city or use lands in a proper way. The Figure above (Fig3) shows an example of an area which it has been demonstrated to be appropriate to build residential houses and green areas, but the eld should contain one-third of green areas at all times. In other words if we have an area that can store 6 buildings, 2 of these must be green areas, the other 4 must be houses.
To represent KB we can de ne two rules such as: 1. In each position is possible to build whether a house or a green area. 2. Desirable number of green areas is equal to the total space divided by 3.
Listing 1.1. Basic Land Use Example in ASP 1 1f h o u s e I n P o s i t i o n (P) , g r e e n A r e a I n P o s i t i o n (P)g1: p o s i t i o n (P ) . 2 1 f houseType (C, P) : house (C) g 1 : h o u s e I n P o s i t i o n (P ) . 3 4 housesNumber (N) : N = #count f h o u s e I n P o s i t i o n (C) g . 5 greenAreasNumber (N) : N = #count f g r e e n A r e a I n P o s i t i o n (C) g . 6 7 desiredNumberOfGreenAreas (A/ 3) : a r e a (A) . 8 : greenAreasNumber (N) , desiredNumberOfGreenAreas (NAV) ,N!=NAV. 9 10 b u i l t ( house ,TC, P) : houseType (TC, P ) . 11 b u i l t ( greenArea , P) : g r e e n A r e a I n P o s i t i o n (P ) .
The Basic Land Use Example code above shows the set of rules and restrictions that arises for KB where lines 1 and 2 talk about the rule 1. Lines 4 and 5 carry the counting houses and green areas. Line 7 calculates the total of green areas to have by dividing the total space by 3 and line 8 restricts that the number of green areas were di erent than the calculated. Finally, lines 10 and 11 indicate where the houses and green areas will be built. On the other hand it is necessary to de ne the current scenario or R1 de ning a rst example indicating that the area is of size 6 and there is only one kind of house to be built.
Listing 1.2. Basic Land Use Example for R1 1 a r e a ( 6 ) . 2 p o s i t i o n ( 1 . . A) : 3 house ( 1 . . 1 ) . 4 5 %% C o n s t r a i n t t h a t i n the 5 th p o s i t i o n a house must be b u i l t 6 %% This can be a bad q u a l i t y land 7 : b u i l t ( greenArea , 5 ) .
%% Area with 6 s l o t s f o r c o n s t r u c t i o n a r e a (A) . %% T h e r e f o r e t h e r e a r e 6 p o s i t i o n s
%% E x i s t 1 type o f house
If only using the rst three lines, we can see that there is a total of 15 solutions combining in the 6 spaces, the number of houses and green areas respecting the corresponding number of green areas. Adding the constraint that the area number 5 is not suitable for a green area construction, so a house must be built. This may satisfy certain qualities of the land mentioned in the previous section. Running this example will deliver a total of 10 solutions. This amount of results could simplify decision-making, but it is possible that in another scenario R2, there are three di erent models of houses to be built. The complexity of this issue has been raised for a total of 1,215 viable results. It is worth to mention that if we add the same constraint listed above, the number of results will decrease to 810.
Listing 1.3. Basic Land Use Example for R2 1 a r e a ( 6 ) . 2 p o s i t i o n ( 1 . . A) : 3 house ( 1 . . 3 ) .
%% Area with 6 s l o t s f o r c o n s t r u c t i o n a r e a (A) . %% T h e r e f o r e t h e r e a r e 6 p o s i t i o n s
%% E x i s t s 3 t y p e s o f h o u s e s
Finally, if later we found a real scenario like R3 expressing a land where ts 9 buildings instead of 6, and applying the same KB, the total results exponentially increase to 61,236. Again, by adding the mentioned constraint we can limit the result to 40,824.
Listing 1.4. Basic Land Use Example for R2 1 a r e a ( 9 ) . 2 p o s i t i o n ( 1 . . A) : 3 house ( 1 . . 3 ) .
%% Area with 9 s l o t s f o r c o n s t r u c t i o n a r e a (A) . %% T h e r e f o r e t h e r e a r e 9 p o s i t i o n s
%% E x i s t s 3 t y p e s o f h o u s e s
In summary, KB has not changed over time but R has exempli ed three di erent cases and the results show an exponential growth leading to an extensive analysis before a decision can be made. The more complex the problem, the more results we can get. It is worth noting that the greater the details modeled in R including constraints, more speci c results we can get, limiting an exponential growth and making easier the analysis of the results and decision-making.
In this paper is presented a new and innovative approach to begin to contribute to the understanding of the urban structure and planning with the help of ASP. Also it is demonstrated that a declarative programming perspective ts properly in the urban problems modeling.
It is worth mentioning that the set of characteristics of an urban society is
manifested in its territorial structure, therefore, each city will have a di erent soil
use structure [
Finally, once advanced the following works where both KB and R are in a higher level of maturity, we will seek to test four hypotheses, which are: Review a real scenario R to determine whether or not this particular zone makes a proper use of lands.
Recommendations or modi cations for R with the purpose of nding alternatives to ful ll a proper land use management.
Projections of how R can be developed in short, medium and long term. Forecasts that show how R could grow if certain changes or adjustments on prior knowledge are not made.