Predicate calculus logic

The multi-valued predicate calculus logic as implemented in QED has been demonstrated to be suitable for cleanly representing strategic axioms of chemical synthesis. QED is a powerful tool for exploring inference in the planning of synthesis strategies. QED helped us elucidate key strategic concepts and their interdependence and... 

First-order predicate calculus admits proof techniques that can be shown to be sound and complete (Lloyd, 1987). The soundness of the proof technique is important because it ensures that our methodology will not deduce results that are invalid. We are less concerned with completeness, because in most cases, although the proof technique will be complete, the theory of dominance or equivalence we have available will be incomplete for most problems. Restricting the first-order logic to be of horn clause form, enables the employment of SLD resolution, a simpler... 

In this chapter we discuss techniques for program verification and their mathematical justification. The basic idea behind these methods was originally presented by Floyd mathematical formulations and logical justifications were developed by Cooper and Manna, and others, and continued in King s Ph.D. thesis in which he presented the development of a partial implementation for these techniques. A sanewhat different axiomatic approach has been pursued by Hoare et al. The reader who has never made acquaintance with the formalism of the first order predicate calculus should at this point turn to Appendix A for a brief and unrigorous exposition of the material relevant to this chapter. 

A Multivalued Logic Predicate Calculus Approach to Synthesis Pla ining... 

In this paper we describe the need for planning, and then develop the predicate calculus we used and the choice of multi-valued logic. Finally we briefly describe the QED program, a few rules, and an example analysis. Other papers in the QED series will cover the program and chemical results in detail. 

We chose the first order predicate calculus (PC) as our language for representing synthetic principles. The first order predicate calculus (PC) is a "formal" system of logic.(11)(12)(13) In this context, formal means that it is the form of the arguments that is important, not the actual content. The term "calculus" comes from the meaning "a method of calculation", and does not refer to Newton s differential calculus. 

These three statements merge two tables, partition a table into two based on a predicate, and copy a table, respectively. Each statement and its inverse can be represented as a logical formula in predicate calculus as well as SQL statements that... 

Clauses are alternative notations of statements expressed in first-order predicate calculus. They have the form of a logical implication. A clause is expressed as a pair of sets of terms in the form... 

Horn clauses do not have the expressive power of the full clausal form of logic and, therefore do not have the power of first-order predicate calculus. The main disadvantage is that it is impossible to represent negative information like Siblings are not married with Horn clauses. 

Predicate calculus is derived from propositional logic, in which propositions or statements can result in one of two values, e.g., true or false. Several logical operators exist to enable propositions to be developed. Some of the most important are ... 

First-Order Predicate Calculus System of formal logic, including Boolean expressions and quantification, that is rich enough to be a language for mathematics and science. 

In 1847, George Boole developed his algebra for reasoning that was the foundation for first-order predicate calculus, a logic rich enough to be a language for mathematics. 

Using the criterion of relevance can be a tragic joke. Perhaps the most ironic of all such developments is to be found in the evolution of mathematical logic and of the theory of sets. These used to be regarded as the most abstruse and esoteric branches of mathematics, rather more of philosophy than of mathematics. Then came the Russell-Whitehead paradox, Goedel s proofs of the completeness of the Predicate Calculus (1930) and of the incompleteness of arithmetic (1931). He used computable... 

A trace y over an ontology Ont and time frame T is a mapping y T STATES (Ont), i.e., a sequence of states Yt (t T) in STATES(Ont). The temporal trace language TTL is built on atoms referring to, e.g., traces, time and state properties. For example, in trace y at time t property p holds is formalised by state(y, t) = p. Here = is a predicate symbol in the language, usually used in infix notation, which is comparable to the Holds-predicate in situation calculus. Dynamic properties are expressed by temporal statements built using the usual first-order logical connectives (such as A, V, = ) and quantification (V and 3 for example, over traces, time and state properties). For example, the informally stated dynamic property introduced above is formally expressed as follows ... 

K. L. Clark and S. Sickel. Predicate logic A calculus for deriving programs. In Proc. oflJCATll, pp. 410-411. 

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