A Logic of Explicit Knowledge - Lehman College
... Now we drop the operator K from the language, and introduce a family of explicit reasons instead— I’ll use t as a typical one. Following [1, 2] I’ll write t:X to indicate that t applies to X—read it as “X is known for reason t.” Formally, if t is a reason and X is a formula, t:X is a formula. Of cou ...
... Now we drop the operator K from the language, and introduce a family of explicit reasons instead— I’ll use t as a typical one. Following [1, 2] I’ll write t:X to indicate that t applies to X—read it as “X is known for reason t.” Formally, if t is a reason and X is a formula, t:X is a formula. Of cou ...
Eliminating past operators in Metric Temporal Logic
... pointwise and continuous versions of the logic. To point out a simple consequence of this result, we recall that the pointwise version of MTL over infinite models was shown to be undecidable [12] via a reduction from channel systems to the general (recursive) version of MTL. From our result above it ...
... pointwise and continuous versions of the logic. To point out a simple consequence of this result, we recall that the pointwise version of MTL over infinite models was shown to be undecidable [12] via a reduction from channel systems to the general (recursive) version of MTL. From our result above it ...
The Logic of Compound Statements
... called proposition forms or formulas built from propositional variables (atoms), which represent simple propositions and symbols representing logical connectives Proposition or propositional variables: p, q,… each can be true or false Examples: p=“Socrates is mortal” q=“Plato is mortal” ...
... called proposition forms or formulas built from propositional variables (atoms), which represent simple propositions and symbols representing logical connectives Proposition or propositional variables: p, q,… each can be true or false Examples: p=“Socrates is mortal” q=“Plato is mortal” ...
Discrete Mathematics
... having a truth value that’s either true (T) or false (F) (never both, neither, or somewhere in between). A proposition (statement) may be denoted by a variable like P, Q, R,…, called a proposition (statement) variable. ...
... having a truth value that’s either true (T) or false (F) (never both, neither, or somewhere in between). A proposition (statement) may be denoted by a variable like P, Q, R,…, called a proposition (statement) variable. ...
PPT
... A proof of Q from H1, H2, … Hk is finite sequence of propositional forms Q 1, Q 2, … Qn such that Qn is same as Q and every Qj is either one of Hi, (i = 1, 2, … , k) or it follows from the proceedings by the logic rules. Note: In these proofs we will follow the following formats: We begin with by li ...
... A proof of Q from H1, H2, … Hk is finite sequence of propositional forms Q 1, Q 2, … Qn such that Qn is same as Q and every Qj is either one of Hi, (i = 1, 2, … , k) or it follows from the proceedings by the logic rules. Note: In these proofs we will follow the following formats: We begin with by li ...
Vectors and Vector Operations
... A relation is transitive if whenever one has both a b and b c then one also has a c. A relation is symmetric if whenever one has a b then one also has b a. A relation is reflexive if a a for every object a. Often it is easy to verify that a certain relation has these three properti ...
... A relation is transitive if whenever one has both a b and b c then one also has a c. A relation is symmetric if whenever one has a b then one also has b a. A relation is reflexive if a a for every object a. Often it is easy to verify that a certain relation has these three properti ...
Introduction to Predicate Logic
... If P is a predicate, then [[P ]] is specified by a function V (in the model M ) that assigns a set-theoretic objects to each predicate. [[P ]]M,g = V (P ) 3. If P is an n-ary predicate and t, ..., tn are all terms (constants or variables), then for any model M and an assignment function g, [[P (t ...
... If P is a predicate, then [[P ]] is specified by a function V (in the model M ) that assigns a set-theoretic objects to each predicate. [[P ]]M,g = V (P ) 3. If P is an n-ary predicate and t, ..., tn are all terms (constants or variables), then for any model M and an assignment function g, [[P (t ...
A Nonstandard Approach to the. Logical Omniscience Problem
... What about logical omniscience? Notice that notions like "validity" and "logical consequence" (which played a prominent part in our informal description of logical omniscience) are not absolute notions; their formal definitions depend on how truth is defined and on the class of worlds being consider ...
... What about logical omniscience? Notice that notions like "validity" and "logical consequence" (which played a prominent part in our informal description of logical omniscience) are not absolute notions; their formal definitions depend on how truth is defined and on the class of worlds being consider ...