How complex are random graphs in first order logic?
نویسندگان
چکیده
منابع مشابه
How complex are random graphs in first order logic?
It is not hard to write a first order formula which is true for a given graph G but is false for any graph not isomorphic to G. The smallest number D(G) of nested quantifiers in a such formula can serve as a measure for the “first order complexity” of G. Here, this parameter is studied for random graphs. We determine it asymptotically when the edge probability p is constant; in fact, D(G) is of...
متن کاملConceptual Graphs and First-Order Logic
Conceptual Structures (CS) Theory is a logic-based knowledge representation formalism. To show that conceptual graphs have the power of rst-order logic, it is necessary to have a mapping between both formalisms. A proof system, i.e. axioms and inference rules, for conceptual graphs is also useful. It must be sound (no false statement is derived from a true one) and complete (all possible tautol...
متن کاملConceptual Graphs and First Order Logic
We study Sowa’s conceptual graphs (CGs) with both existential and universal quantifiers. We explore in detail the existential fragment. We extend and modify Sowa’s original graph derivation system with new rules and prove the soundness and completeness theorem with respect to Sowa’s standard interpretation of CGs into first order logic (FOL). The proof is obtained by reducing the graph derivati...
متن کاملFirst-Order Logic on CPDA Graphs
We contribute to the question about decidability of firstorder logic on configuration graphs of collapsible pushdown automata. Our first result is decidability of existential FO sentences on configuration graphs (and their ε-closures) of collapsible pushdown automata of order 3, restricted to reachable configurations. Our second result is undecidability of whole first-order logic on configurati...
متن کاملHow to Prove Higher Order Theorems in First Order Logic
In this paper we are interested in using a first order theorem prover to prove theorems that are formulated in some higher order logic. To this end we present translations of higher order logics into first order logic with flat sorts and equality and give a sufficient criterion for the soundness of these translations. In addition translations are introduced that are sound and complete with resp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random Structures and Algorithms
سال: 2005
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20049