03_Artificial_Intelligence-PredicateLogic
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
Modal Logic
... The canonical frame for System K is the pair Fk = (Wk,Rk) where (1) Wk = {X | X is an MCS } (2) If X and Y are MCSs, then X Rk Y iff {❏X} Y. The canonical model for System K is given by Mk = (Fk,Vk) where for each X Wk, Vk(X) = X P. Lemma For each MCS X Wk and for each formula ,Mk ...
... The canonical frame for System K is the pair Fk = (Wk,Rk) where (1) Wk = {X | X is an MCS } (2) If X and Y are MCSs, then X Rk Y iff {❏X} Y. The canonical model for System K is given by Mk = (Fk,Vk) where for each X Wk, Vk(X) = X P. Lemma For each MCS X Wk and for each formula ,Mk ...
Predicate logic
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
... • We'd like to conclude that Jan will get wet. But each of these sentences would just be a represented by some proposition, say P, Q and R. What relationship is there between these propositions? We can say P /\ Q → R Then, given P /\ Q, we could indeed conclude R. But now, suppose we were told Pat i ...
Monadic Predicate Logic is Decidable
... • Let the signature of d in D (henceforth sig(d)) be the sequence where ji=1 if M
specifies that Pi is true of d and ji=0 otherwise
– sig(d) tell us which predicates in S are true of d
– given S, there are exactly 2k different possible
...
... • Let the signature of d in D (henceforth sig(d)) be the sequence
1.3.4 Word Grammars
... More or less all sets of objects in computer science or logic are defined inductively. Typically, this is done in a bottom-up way, where starting with some definite set, it is closed under a given set of operations. Example 1.5.1 (Inductive Sets). In the following, some examples for inductively defi ...
... More or less all sets of objects in computer science or logic are defined inductively. Typically, this is done in a bottom-up way, where starting with some definite set, it is closed under a given set of operations. Example 1.5.1 (Inductive Sets). In the following, some examples for inductively defi ...
CSE596, Fall 2015 Problem Set 1 Due Wed. Sept. 16
... for a proof of having followed the discussion, which can be a brief “bottom-line conclusion” in your own words, and it will have 3 pts. of “checkoff credit” (graded for showing a basic understanding but not fullness or accuracy). Here, however, the bottom-line is a preview of things to come (much) l ...
... for a proof of having followed the discussion, which can be a brief “bottom-line conclusion” in your own words, and it will have 3 pts. of “checkoff credit” (graded for showing a basic understanding but not fullness or accuracy). Here, however, the bottom-line is a preview of things to come (much) l ...
predicate
... • ⊨ holds iff for all models M and lookup tables l, whenever M ⊨l holds for all then M ⊨l holds as well • is satisfiable iff there is some model M and lookup table l such that M ⊨l holds • is valid iff M ⊨l holds for all models M and lookup tables l ...
... • ⊨ holds iff for all models M and lookup tables l, whenever M ⊨l holds for all then M ⊨l holds as well • is satisfiable iff there is some model M and lookup table l such that M ⊨l holds • is valid iff M ⊨l holds for all models M and lookup tables l ...
Lecture Notes 2
... to contradiction”. To prove a proposition x it’s sufficient to assume the negation ¬x of x and deduce from ¬x two contradictory statements, say, y and ¬y. The the above tautology implies that x is true. Many mathematical theorems can be formally described by an implication x → y. Call this implication ...
... to contradiction”. To prove a proposition x it’s sufficient to assume the negation ¬x of x and deduce from ¬x two contradictory statements, say, y and ¬y. The the above tautology implies that x is true. Many mathematical theorems can be formally described by an implication x → y. Call this implication ...
F - Teaching-WIKI
... • One of the simplest and most common logic – The core of (almost) all other logics ...
... • One of the simplest and most common logic – The core of (almost) all other logics ...
02_Artificial_Intelligence-PropositionalLogic
... • One of the simplest and most common logic – The core of (almost) all other logics ...
... • One of the simplest and most common logic – The core of (almost) all other logics ...
F - Teaching-WIKI
... • One of the simplest and most common logic – The core of (almost) all other logics ...
... • One of the simplest and most common logic – The core of (almost) all other logics ...
Notes on Propositional Logic
... leading to the notion of propositional atoms, described in the following section. For traditional logic, we have considered particular forms of arguments that combine propositions. For example, If p1 then p2 . We would like to study in what ways propositions can be combined into arguments, which wil ...
... leading to the notion of propositional atoms, described in the following section. For traditional logic, we have considered particular forms of arguments that combine propositions. For example, If p1 then p2 . We would like to study in what ways propositions can be combined into arguments, which wil ...