Inclusive Disjunction Research Articles

Symbolic Logic: A Razor-Edged Tool for Drafting and Interpreting Legal Documents

A large amount of the litigation based on written instruments?whether statute, contract, will, conveyance or regulation?can be traced to the draftsman's failure to convey his meaning clearly. Frequently, of course, certain items may purposely be left ambiguous, but often the question in issue is due to an inadvertent ambiguity that could have been avoided had the draftsman clearly expressed what he intended to say. In this Article it is suggested that a new approach to drafting, using certain elementary notions of symbolic logic, can go a long way towards eliminating such inadvertent ambiguity. This new approach makes available to draftsmen a technique that achieves some of the clarity, precision and efficiency of analysis that symbolic logic provides. In addition, it can be a valuable aid in moving towards a more comprehensive and systematic method of interpretation,1 as well as drafting. This approach is a compromise between expression in ordinary prose and expression in the mathematical notation of symbolic logic?enough like ordi? nary prose to be understood easily by any careful reader, enough like sym? bolic logic to achieve some of its important advantages. It represents an effort to adapt some of the techniques of symbolic logic to make more systematic what is now best described as the "art" of drafting. The first section will explain six elementary logical connectives: implication, conjunction, coimplication, exclusive disjunction, inclusive disjunction and negation. In order to simplify this exposition, trivial examples will be used for purposes of illustration. In the second section the proposed system will be applied to actual legal problems of drafting, interpretation, simplification and comparison. Six Elementary Logical Connectives 2 1.0 Implication The development of a more systematic method of drafting will enable the lawyer to communicate his intended meaning more effectively. That is the basic proposition to which this Article is addressed. This same proposition can be stated in a different form:

SYMBOLIC LOGIC: A RAZOR-EDGED TOOL FOR DRAFTING AND INTERPRETING LEGAL DOCUMENTS

A large amount of the litigation based on written instruments?whether statute, contract, will, conveyance or regulation?can be traced to the draftsman's failure to convey his meaning clearly. Frequently, of course, certain items may purposely be left ambiguous, but often the question in issue is due to an inadvertent ambiguity that could have been avoided had the draftsman clearly expressed what he intended to say. In this Article it is suggested that a new approach to drafting, using certain elementary notions of symbolic logic, can go a long way towards eliminating such inadvertent ambiguity. This new approach makes available to draftsmen a technique that achieves some of the clarity, precision and efficiency of analysis that symbolic logic provides. In addition, it can be a valuable aid in moving towards a more comprehensive and systematic method of interpretation,1 as well as drafting. This approach is a compromise between expression in ordinary prose and expression in the mathematical notation of symbolic logic?enough like ordi? nary prose to be understood easily by any careful reader, enough like sym? bolic logic to achieve some of its important advantages. It represents an effort to adapt some of the techniques of symbolic logic to make more systematic what is now best described as the art of drafting. The first section will explain six elementary logical connectives: implication, conjunction, coimplication, exclusive disjunction, inclusive disjunction and negation. In order to simplify this exposition, trivial examples will be used for purposes of illustration. In the second section the proposed system will be applied to actual legal problems of drafting, interpretation, simplification and comparison. Six Elementary Logical Connectives 2 1.0 Implication The development of a more systematic method of drafting will enable the lawyer to communicate his intended meaning more effectively. That is the basic proposition to which this Article is addressed. This same proposition can be stated in a different form:

Algebra of Neural Nets

A paper showing the application of modern mathematics in modern biophysics. As example Boolean algebra is shown as applied to neural nets. Boolean algebra is a new algebra that was initiated by George Boole in 1854 with publication of his Laws of Thought. In the modern notation it goes like this: let a closed curve A denote a set of objects while another clQsed curve B denotes another set of objects. If the two sets have objects in common the two curves overlap as in the figure. Instead of a sum we think of a union of sets A and B meaning the set of all objects in A or B or both. Boole originally excluded the both part of this A concept thus obtainingwhat is now called modulo two addition. His idea survives Figur* in analysis situs, in formal logic as exclusive disjunction and other places where modulo two addition is used. The overlap or common part is called the intersection of the sets A and B. And we write AUI for the union and AnB for the intersection of the sets.A and B. Intersection then is the equivalent of multiplication. Then we have the notion of inclusion. When I write AfnB C A I mean that the common part of A and B is contained in A. Also AfnB =B and AnB =AU B. So the intersection is a subset of the union of A and B. Likewise I can write A U B D A meaning that the union of A and B contains A. The algebra of neural nets is couched in the notation of the propositional calculus so we will have to transfer our ideas into the isomorphic calculus. The symbols in the propositional calculus are called sentential connectives. Tlhus we have the isomorphism: Algebra of Sets Propositional Calculus = inclusion = implication U union _ inclusive disjunction n intersection ( )( ) conjunction juxtaposition equals equivalence CA in S complement denial -A, not A The biconditional is interpreted like this: implication is called the conditional so A nB or A implies B and BMA or B implies A This content downloaded from 207.46.13.58 on Wed, 12 Oct 2016 04:40:39 UTC All use subject to http://about.jstor.org/terms