First-order logic. A theory about some topic is usually first-order logic together with a specified domain of discourse over which the quantified variables range, finitely many functions which map from that domain into it, finitely many predicates defined on that domain, and a recursive set of axioms which are believed to hold for those things. Sometimes "theory" is understood in a more formal sense, which is just a set of sentences in first-order logic. The adjective "first-order" distinguishes first-order logic from higher-order logic in which there are predicates having predicates or functions as arguments, or in which one or both of predicate quantifiers or function quantifiers are permitted.[1] In first-order theories, predicates are often associated with sets.
In interpreted higher-order theories, predicates may be interpreted as sets of sets. First-order logic is the standard for the formalization of mathematics into axioms and is studied in the foundations of mathematics. Introduction[edit] . X in . Enterprise. View topic - Universal Constructor Based Spaceship. A new age of Game of Life exploration and design! I agree with Nick. This marks an important turning point in Life technology, comparable to the discovery of the Gosper Glider Gun and stable Herschel tracks. What is the range of velocities that can be achieved in this way? Any velocity less than c/2 (by the L1, or Manhattan metric) can be attained by a Universal constructor.
The proof is quite long-winded, so I won't mention it unless you are interested. For each velocity, what are the smallest spaceships (by various definitions of "smallest")? A spaceship of period n, where n is equal to or greater than a constant, can have diameter of O(sqrt(log(n))). How about rakes, guns, puffers, breeders based on such spaceships, and/or constructing them? Gemini can be trivially modified into a rake, puffer or breeder. Producing a Gemini gun is more difficult, but not totally intractable. How readily can changes in velocity be programmed into such a ship? To an arbitrary degree of accuracy, in fact.
Conceptual Graphs Home Page. Challenges for Ontology Design. Author: Thomas GruberTitle: Grande Challenges for Ontology Design (or is it Vente?) Date: March 1, 2007Type: Invited presentation Citation: Tom Gruber (2007). Grande Challenges for Ontology Design (or is it Vente?). Presentation to Ontolog, March 1, 2007. File: challenges-for-ontology-design.ppt Context: Monthly presentation at international conference call of the Ontolog Community in which participants interact over synchornous and asynchronous communication. Abstract: Why bother with ontology design, particularly when it involves the trouble of collaborating with other people and their peculiar ideas? In this session I will frame a discussion about ontology design, using the model of engineering design that has brought tremendous success to electronic and physical engineering disciplines, and to some extent software engineering.