Harland, J. (1997). On goal-directed provability in classical logic. Computer Languages, 23:161--178.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....conclusions [Miller, 1994, Miller, 1996] then any modal theorem has a uniform proof in a lifted, explicitly scoped inference system. Put another way, explicitly scoped inference assimilates modal proof to classical proof, and we know that uniformity is not really a restriction on classical proof [Harland, 1997, Nadathur, 1998] This is why my investigation emphasizes questions of information flow, such as modularity and locality, rather than questions of goal directed proof per se. I will refer to the proof of Figure 4 to illustrate some of the properties of information flow in goal directed search. ....

Harland, J. (1997). On goal-directed provability in classical logic. Computer Languages, 23:161--178.

....following problem is encountered: if the righthand side of a sequent contains two or more non atomic formulas, how should the logical connectives at the head of those formulas be introduced There seems to be two choices. One choice simply requires that one of the possible introductions be done [12]. This choice has the disadvantage that there might be interdependencies between right introduction rules: thus, the meaning of the logical connectives in the goal would not be reflected directly and simply into the structure of a proof, a fact that complicates the operational semantics of the ....

James Harland and David Pym. On goal-directed provability in classical logic. Technical Report 92/16, Dept of Comp Sci, Uni. of Melbourne, 1992.

....following problem is encountered: if the right hand side of a sequent contains two or more non atomic formulas, how should the logical connectives at the head of those formulas be introduced There seems to be two choices. One choice simply requires that one of the possible introductions be done [10]. This has the disadvantage that there might be an interdependency between rightintroduction rules in that one may need to appear lower in a proof than another, in which case, logical connectives in the goal would not be reflected directly and simply into the structure of the proof. A second ....

J. Harland and D. Pym. On Goal-directed Provability in Classical Logic. Technical report 92/16, Dept. of Computer Science, Univ. of Melbourne, 1992.

....proofs is complete. The properties of such proofs have been thoroughly investigated for various fragments of first and higher order intuitionistic logic (for Horn clauses and for a generalisation of them known as hereditary Harrop formulas [17] as well as for fragments of classical logic [19, 8] and linear logic [12, 1, 2, 21] These analyses exhibit many points of similarity, as well as some specific points of difference, which can generally be traced to particular inference rules and their properties. For example, linear logic inherits a number of the properties of the classical ....

Harland J. On Goal-Directed Provability in Classical Logic, Computer Languages 23:24: 161-178, 1997.

....and what the results of the previous analysis would be. This is a particularly interesting question given that there has been a significant amount of investigation of notions of goal directed provability for multiple conclusioned systems such as linear logic [1, 15, 19, 21] and classical logic [10, 18]. Thus it seems appropriate to investigate the design of logic programming languages via goal directed provability for a multiple conclusioned system for intuitionistic logic, and to compare the results with the single conclusioned case. 2 Preliminaries 2.1 Sequent Calculi Sequent calculi are ....

J. Harland. On Goal-Directed Provability in Classical Logic. Computer Languages, 23:161-- 178, 1997.

....and what the results of the previous analysis would be. This is a particularly interesting question given that there has been a significant amount of investigation of notions of goal directed provability for multiple conclusioned systems such as linear logic [1, 15, 19, 21] and classical logic [10, 18]. Thus it seems appropriate to investigate the design of logic programming languages via goal directed provability for a multiple conclusioned system for intuitionistic logic, and to compare the results with the single conclusioned case. 2 Preliminaries 2.1 Sequent Calculi Sequent calculi are ....

J. Harland. On Goal-Directed Provability in Classical Logic. Computer Languages, 23:161-- 178, 1997.

....systems, and what the results of the previous analysis would be. This is a particularly interesting question given that there has been a significant amount of investigation of notions of goaldirected provability for multiple conclusioned systems such as linear logic [1, 10, 19] and classical logic [8, 17, 18]. Thus it seems appropriate to investigate the design of logic programming languages via goal directed provability for a multiple conclusioned system for intuitionistic logic, and to compare the results with the single conclusioned case. In this paper we investigate multiple conclusioned sequent ....

J. Harland. On Goal-Directed Provability in Classical Logic. Computer Languages, 23:161--178, 1997.

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