Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... the modality 3< ϕ is not definable in terms of 3≤ ϕ – even though the strict relation ≺ is first-order defined in terms of . It is easy to draw two pointed models which are bisimilar in the above sense with respect to the clauses for the weak order, while the truth value of some formula 3< ϕ differ ...
... the modality 3< ϕ is not definable in terms of 3≤ ϕ – even though the strict relation ≺ is first-order defined in terms of . It is easy to draw two pointed models which are bisimilar in the above sense with respect to the clauses for the weak order, while the truth value of some formula 3< ϕ differ ...
Predicate logic definitions
... Proof-Theoretic Concepts A derivation in PDE is a series of sentences of PLE, each of which is either an assumption or is obtained from previous sentences by one of the rules of PDE. A sentence P of PLE is derivable in PDE from a set Γ of sentences of PLE, written S ` P, iff there exists a derivatio ...
... Proof-Theoretic Concepts A derivation in PDE is a series of sentences of PLE, each of which is either an assumption or is obtained from previous sentences by one of the rules of PDE. A sentence P of PLE is derivable in PDE from a set Γ of sentences of PLE, written S ` P, iff there exists a derivatio ...
Default Logic (Reiter) - Department of Computing
... Given E, the reduct DE is a (possibly empty) set of ordinary, non-default, monotonic rules. So we have available all the properties of (monotonic, non-default) closures. For example: E is an extension of (D, W ) when E is the smallest set of formulas S such that: S = Th(W ∪ TDE (S) ) And we have var ...
... Given E, the reduct DE is a (possibly empty) set of ordinary, non-default, monotonic rules. So we have available all the properties of (monotonic, non-default) closures. For example: E is an extension of (D, W ) when E is the smallest set of formulas S such that: S = Th(W ∪ TDE (S) ) And we have var ...
Reasoning about Communication Graphs Eric Pacuit Rohit Parikh July 19, 2006
... value of q. In this case i has learned more than p ∨ q, i has learned p as well. For the only way that j could have known p ∨ q is if j knew p in which case p must be true. Our definition of the semantics below will address both these issues. We first introduce the notion of i-equivalence among hist ...
... value of q. In this case i has learned more than p ∨ q, i has learned p as well. For the only way that j could have known p ∨ q is if j knew p in which case p must be true. Our definition of the semantics below will address both these issues. We first introduce the notion of i-equivalence among hist ...
MATH 8253 ALGEBRAIC GEOMETRY HOMEWORK 1 1.2.10. Let A
... is flat over A if and only if B = A. One can show that this result is true without the assumption of finiteness of B over A. First we prove a lemma. Lemma 1. Let C be any subring of Frac(A) containing A. Then C is free as an A-module if and only if C = A. Proof. The “if” part is trivial. So assume C ...
... is flat over A if and only if B = A. One can show that this result is true without the assumption of finiteness of B over A. First we prove a lemma. Lemma 1. Let C be any subring of Frac(A) containing A. Then C is free as an A-module if and only if C = A. Proof. The “if” part is trivial. So assume C ...
John L. Pollock
... set theory is generally developed as a foundation for mathematics. One begins with obscure axioms and derives formal theorems in a rigorous but unintuitive manner, with the ultimate objective of constructing theories of infinite cardinals and transfinite ordinals. For nontechnical philosophers, the ...
... set theory is generally developed as a foundation for mathematics. One begins with obscure axioms and derives formal theorems in a rigorous but unintuitive manner, with the ultimate objective of constructing theories of infinite cardinals and transfinite ordinals. For nontechnical philosophers, the ...
logic for the mathematical
... Actually, in that argument, the word “should” is probably better left out. Mostly, we want to deal with statements which simply state some kind of claimed fact, statements which are clearly either true or false, though which of the two might not be easy to determine. Such statements are often called ...
... Actually, in that argument, the word “should” is probably better left out. Mostly, we want to deal with statements which simply state some kind of claimed fact, statements which are clearly either true or false, though which of the two might not be easy to determine. Such statements are often called ...
