### Table 1. Introduction rules, elimination rules and ?:; ?

"... In PAGE 5: ..._, implication !, universal quanti er 8 and existential quanti er 9 are exactly as the ones in classical logic [14]. Therefore, they will not be here presented, but the additional rules can be found in Table1 . For paraconsistent negation we have an introduction rule I: and an elimination rule E:, but E: deals only with ?-free formulas.... ..."

### Table 6: Introduction rules for the logical operations.

### Table 2 : clues and rules for introductions processing

### Table 1: Price Limits(a) in Exchanges in the World Country Stock Exchange Price Limit and/or circuit breakers

"... In PAGE 1: ...Price Limits Li Gan and Dong Li Department of Economics University of Texas Austin, TX 78712 February, 2001 1 Introduction Many stock exchanges set up certain limits on the maximum variation that a stock is allowed to have in a single day. Table1 gives an overview of the price limit rules of some of the world exchanges. As reflected in the table, among stock exchanges in 41 countries that we obtain information, 23 of them have price limits and 7 of them have some kinds of circuit breaker rules.... ..."

### Table 4: Introduction of a cache Operator (Second Rule)

"... In PAGE 45: ... The second transformation rule pushes an introduced cache operator up, so as to ensure that it completely covers the largest possible replicated subplan. As depicted in Table4 , it promotes a cache operator by swapping it with its parent, provided that its sibling is also a scan marked by the same token. Eventually, after su cient applications of this rule, the cache operator is the parent of a subplan that encompasses all scan operators associated with the same CID inference rule as desired.... ..."

### Table 1. Sequent and anti-sequent left rules - Introduction into antecedent

### Table 5. Content of cluster Introduction/- explanation of meeting process amp; rules . Cluster Introduction/explanation of meeting process amp; rules

### Table 1 Introduction Dates for Energy Derivative Contracts

"... In PAGE 7: ...ng on the crude oil market. Section VI provides a summary and conclusions. II. Data and Preliminary Analysis Table1 lists the primary energy futures and futures option contracts , along with their respective introduction dates. Each of these contracts is traded at either the New York Mercantile Ex- change (NYMEX) or the International Petroleum Exchange (IPE).... In PAGE 19: ...following the first derivative introduction and they should decay with subsequent introduc- tions as the market gradually becomes more complete. To investigate these issues, we apply our methodology to each of the subsequent i n tro- duction dates reported in Table1 . The only difference is that each of these introductions occurs after the start of our daily crude oil price series, so we use the daily prices ( rather than weekly) in this analysis.... ..."

### Table 1. De nition Introduction Phase

2002

"... In PAGE 9: ...nnermost (i.e., ti does not contain operation-rooted subterms) such that each one of them shares at least a common variable with at least one more subterm in T 2. Apply the DEFINITION INTRODUCTION RULE to generate : Rdef = (fnew(x) ! T) where fnew is a new function symbol not appearing R, and x is the set of variables of T OUTPUT: Definition Rule (Eureka) Rdef In order to avoid these risks, our approach generates eureka de nition following a very simple strategy ( Table1 ) that obtains similar levels of generality than pre- vious approaches and covers most practical cases. The main advantages are that the analysis is terminating, easy and quickly, and does not perform redundant calculus (like unfolding steps, instantiations, etc.... In PAGE 9: ...) that properly corresponds to subsequent phases. As illustrated by step 1 in Example 2, our eureka generator proceeds as the algorithm in Table1 shows. Observe that the input of the algorithm is the original program R and a selected rule R 2 R which de nition is intended to be 4 This fact is observed during the so-called quot;program extraction phase quot; in [20].... In PAGE 13: ...contrast with the previous case, where an optimal de nition of fnew is obtained, now the process tries with rules in R in order to replace and reuse as much as possible the optimized de nition of fnew into the original program R. In particular, we know that there exists at least a rule R = (l ! r) 2 R (the one considered in Table1 to generate de eureka Rdef) that veri es TEST(R; Rdef)=2. Hence, similarly as done before, we can apply an abstraction and folding steps to it, obtaining the new rule: l ! r[zj]Pj where hz1; : : : ; zni = fnew(x): where the call to fnew enhances the nal de nition of the old function symbol that roots l.... ..."