In the arid and semi-arid area's rainfall have considerable changes in terms of time and amount that make the water resource management an important issue. In this research, using both BOOLEAN and Fuzzy logic were zoned potentiality suitable areas for construction of underground dams. The study area is located in the central region of Ardabil province with 7461 km2 area and semi-arid climate. For this purpose, were used many criteria consist of topography, geology, land use, geomorphology, water quality and quantity, depth of alluvial, and channels ranking. In the BOOLEAN logic method, after preparing the related criteria, suitable and unsuitable areas were determined in two classes 0 and 1 that were combined using AND operator. In the Fuzzy logic method, the criteria were prepared in many classes and scored from 0 to 1 regarding previous researches and area conditions, then the criteria were combined with Fuzzy gamma operator. There is a good accordance between used criteria and combined maps that obtained from two methods. Overall central area and part of southwest and northern area determined as suitable locations for construction of underground dams. Results of Fuzzy logic showed that in the study area, the streams with 3 rank and deep alluvial areas have a high potentiality for underground dams’ construction. Therefore, these areas should be considered as the suitable areas for underground dams.

Irregular patterns of precipitations from temporal as well as spatial perspectives not only cause destructions but also waste surface water resources. Hence, controlling surface water and leading the flood to underground stores improve the efficiency of water usage. Selecting appropriate sites for optimal use of water floods is one of the most important factors in recharging underground water tables in dry lands where the agricultural and rangelands are vulnerable. Traditional methods of site selections are, however, time consuming and error prone. This paper attempts to; analyze existing schemes of site selection; introduces an appropriate method of locating flood-spreading sites using Geospatial Information System; implements the strategy in a case study; and scientifically assesses its results. The study area of this research is Samal sub-basin covering 31571.7 ha of Ahrom basin in Boushehr province. In the present research, factors pertain to earth sciences (quaternary units, slope and landuse) and hydrology (runoff infiltration rate and aquifers’ depth) are considered. Information layers are weighted, classified and integrated through several models such as BOOLEAN LOGICS, index overlay and fuzzy LOGICS. The results are then checked against the existing sites to estimate their accuracy. The results of this research demonstrated that fuzzy logic operators including gamma=0.1, gamma=0.2 and products of fuzzy LOGICS yield the best when compared to control fields and therefore, the models are introduced as the most suitable site selection strategies for flood spreading.

This paper presents a new method for simplification of BOOLEAN functions based on BOOLEAN differences. The proposed method is applicable to various forms of BOOLEAN functions, including truth tables and Binary Decision Diagrams (BDDs). The BOOLEAN differences are extended to cover the truth tables with don't-care components and cutset graphs in BDDs. The results of simplification agree with Quine-McCluskey and ESPRESSO methods. Experimental tests on MCNC and Berkeley PLA benchmarks show that the proposed method gains a performance of 1.5-10 times faster than ESPRESSO. The algorithms of the proposed method are implemented in Java/Perl/C++, and a toolset for logic function simplification is developed.

Standard completeness, completeness on the real unit interval $[0,1]$, is one of important research areas in mathematical fuzzy logic. Recently, standard completeness for semilinear LOGICS with knotted axioms has been investigated \emph{proof-theoretically} by introducing and eliminating density rule. This paper introduces \emph{model-theoretic} completeness for such LOGICS. To this end, it is first shown that knotted axioms can be divided into left and right ones and then proved that mianorm-based logic systems with left and right knotted axioms are standard complete. This completeness is provided by embedding linearly ordered algebras into densely ordered ones and these algebras again into $[0,1]$. More exactly, mianorm-based systems with left and right knotted axioms and their algebraic structures are first discussed. After some examples of mianorms satisfying left and right knotted properties are introduced, standard completeness for those LOGICS is established model-theoretically using the above construction. Finally, this investigation is extended to their corresponding involutive fixpointed systems.

Recently, Morteza Hajhosseini (2023) published his second edition of the book (2017) Two Non-Classical Logic Systems, A new Outlook on Elements of Logic, where he developed various non-standard logical systems based on specific philosophical foundations. His systems consist of the following five: A truth-functional propositional system, A non-truth-functional propositional system, Adding the non-truth-functional implication of the second system to the whole first one, Adding the truth-functional conjunction and disjunction of the first system to the whole second one, Combining the whole two systems into a new comprehensive propositional.

In this paper we continue development of formal theory of a special class of fuzzy LOGICS, called EQ-LOGICS. Unlike fuzzy LOGICS being extensions of the MTL-logic in which the basic connective is implication, the basic connective in EQ-LOGICS is equivalence. Therefore, a new algebra of truth values called EQ-algebra was developed. This is a lower semi lattice with top element endowed with two binary operations of fuzzy equality and multiplication. EQ-algebra generalizes residuated lattices, namely, every residuated lattice is an EQ-algebra but not vice-versa.In this paper, we introduce additional connective D in EQ-LOGICS (analogous to Baaz delta connective in MTL-algebra based fuzzy LOGICS) and demonstrate that the resulting logic has again reasonable properties including completeness.Introducing D in EQ-logic makes it possible to prove also generalized deduction theorem which otherwise does not hold in EQ-LOGICS weaker than MTL-logic.

One of the nice properties of the first-order logic is the compactness of satisfiability. It states that a finitely satisfiable theory is satisfiable. However, different degrees of satisfiability in fuzzy LOGICS will pose various kinds of compactness in these LOGICS.In this article, after an overview on the results around the compactness of satisfiability and compactness of $K$-satisfiability in H\'{a}jek Basic logic, some new results are given around this issue.It will be shown that there are topologies on $[0,1]$ and $[0,1]^2$ for which the interpretation of all logical connectives of the Basic logic is continuous. Furthermore, a topology on first-order structures will be introduced for any similarity relation as well. Then by the same ideas as in continuous logic, the results around the compactness of satisfiability will be extended for Basic logic.