B. Fronhofer. Linearity and plan generation. New Generation Computing, 5:213--225, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....connection proof for a a a as we are not allowed to contract the right subformula a a to a or to weaken the left subformula to a a . In other words, the symbol has a different meaning in the linear connection method than usual. There are a couple of related problems which are discussed in [12]. Obviously, each linear connection proof is a connection proof but there are connection proofs which are not linear. Hence, if we find a linear connection proof for (3.1) then this is also a connection proof for (3.1) and, by the completeness of the connection method [3] we can conclude that ....

B. Fronhofer. Linearity and plan generation. New Generation Computing, 5:213--225, 1987.

.... Gamma A Gamma 0 B Gamma; Gamma 0 A Omega B r Omega Table 1: The multiplicative linear sequent calculus to simulate classical conjunctive planning. like planning still lacks a real logical framework. Recently, the concept of linearity has been shown to be useful for plan generation [4]. In refusing both weakening and contraction, linear logic [5] structurally handles this concept. It was then logical to attempt to introduce linear logic as a logic for plan generation. However, Masseron et al. s formalization concentrated on expressing the adequacy between proofs and actions. ....

B. Fronhofer, Linearity and Plan Generation, New Generation Computing 5 (1987), pages 213-- 225.

....connection proof for a a a as we are not allowed to contract the right subformula a a to a or to weaken the left subformula to a a . In other words, the symbol has a different meaning in the linear connection method than usual. There are a couple of related problems which are discussed in [12]. Obviously, each linear connection proof is a connection proof but there are connection proofs which are not linear. Hence, if we find a linear connection proof for (3.1) then this is also a connection proof for (3.1) and, by the completeness of the connection method [3] we can conclude that ....

B. Fronhofer. Linearity and plan generation. New Generation Computing, 5:213--225, 1987.

....only once) He has been criticised on semantic grounds, namely that since a semantics for the linearization is not known, it constitutes no more than a clever trick of unclear virtue. Later Bibel et al. 33] gave a semantics for this method. Further development of this method was done by Fronhofer [56, 57]. A series of works with an emphasis on an equational implementation of the idea is one by Josef Schneeberger, Steffen Holldobler and his students at Techniche Hochschule Darmstadt [86, 87, 78, 79] They represent the components of state as a multiset term held together by an ....

B. Fronhofer. Linearity and plan generation. New Generation Computing, 5:213--225, 1987.

....is formulated which expresses that from the initial situation the goal situation can be reached. The planning problem then is the problem of deriving a plan by proving this specification formula. Frequently this process is formulated in some non classical logic formalism, for example linear logic [2, 5, 12] or temporal logic [18] or is based on some logical action theory. In the other approach, the planning process is carried out in an algorithmic way [19, 7, 6, 20] Our approach to deductive planning is situated between these two groups. As in all deductive approaches, we start from a logical ....

B. Fronhofer. Linearity and plan generation. New Generation Computing, 5:213--225, 1987.

....over to the goal state. In his first paper, however, Bibel presented his idea in a rather informal way and left out various aspects, especially the question of semantics. This gave rise to many subsequent publications which elaborated the approach and carefully studied the open problems (e.g. [10, 4, 27, 11]) In 1987 Girard published his work on linear logic [12] The main idea behind this approach is to consider certain atomic formulas as resources. This implies that the truth values of formulas may depend on how often certain subformulas occur. In order to achieve this characteristic Girard ....

B. Fronhofer. Linearity and Plan Generation. New Generation Computing, 5:213--225, 1987.

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