1
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2answers
85 views

How to determine whether a set of propositions is consistent?

Definition of consistency is: A set of formulas ⊆ WFF is consistent iff there is no A ∈ WFF such that Σ ⊢ A and Σ ⊢ (¬A). Say you have a set of propositions statements (i.e. $A \lor B \rightarrow C$, ...
1
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1answer
43 views

Help solving a challenge - relational algebra or second order logic

I am a self-taught man and I'm posting my first question here. I'm facing a challenge I'd like to solve. Based on what I know it fits propositional calculus (hope it is). Suppose 3 people: a ...
0
votes
1answer
40 views

Confusion in Conjunctive normal forms

Which of the Following is TRUE about formulae in Conjunctive Normal form? For any formula, there is a truth assignment for which at least half the clauses evaluate true. For any formula, there is a ...
1
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2answers
91 views

First-order logic: how-to produce interpretation where a given formula is false?

For example, given Theory T with predicates $$A(x), B(x), C(x,y), D(x,y), x=y$$ axioms $$\exists x.A(x) \land \exists x.B(x) \land \exists xy.C(x,y)\\ \forall x(A(x) \leftrightarrow \neg B(x)),$$ ...
2
votes
0answers
39 views

Expressing schedule of reinforcement rule using mathematical logic

I am trying to formalize the rules for application of different schedules in a reinforcement learning in special education. Children learn through trials. Each trial is successful if the child ...
2
votes
1answer
142 views

What are some practical applications of mathematical/formal logic to science and humanities? [closed]

I am studying a bit of this and so far it seems that, apart from math and computer science, the discipline of Logic is very self facing, with logicians proving things for other logicians. It left me ...
1
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1answer
183 views

Tracing a most-general unifier algorithm

I'm trying to trace the algorithm for getting the most general unifier, and I'm a bit confused. Can there be more than one solution? (although the adjective 'most' suggests otherwise) found online: ...
3
votes
1answer
56 views

DPLL Algorithm $ \rightarrow $ Resolution proof $ \rightarrow $ Craig Interpolation

I really need help here for an exam that I got tomorrow .. Let's say I got a bunch of constraints: $ c1 = { \lnot a \lor \lnot b } \\ c2 = { a \lor c } \\ c3 = { b \lor \lnot c } \\ c4 = { \lnot b ...
0
votes
1answer
51 views

Making first order logic statements

I'm working on an assignment that deals with predicate calculus, and I'm trying to put sentences into first order logic statements. I've got the hang of most of them, but I'm not quite sure how to do ...
0
votes
1answer
101 views

Constructing Proof Trees for Natural Deduction

I'm in the process of learning the process of writing so-called proof trees for $\textit{Natural Deduction}$. One question that I still grapple with is the actual process According to Van Dalen ...
6
votes
1answer
408 views

Relationship between propositional logic, first-order logic, second-order logic higher-order logic, and type theory

I understand there is propositional logic, first-order logic, second-order logic higher-order logic, and type theory, where the latter logics are extensions of the former logics. Can someone explain ...
0
votes
1answer
256 views

Is first-order logic more expressive than propositional logic with infinite statements?

I read that the difference between propositional logic and first-order logic is that in the latter, we can quantify over individual objects. However, if infinitely long statements are allowed, it ...
1
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1answer
273 views

Propositional Logic and First-Order Logic

I am having a hard time distinguishing between the two different logics. If we consider the statement, “Squares adjacent to the Wumpus are smelly,” and are asked to express it as First-Order Logic, ...
4
votes
1answer
82 views

Some doubts about interpretation of an atomic formula in predicate calculus

I have some doubt related to the interpretation of atomics formulas in predicate calculus. In predicate calculus a formula will be interpreted on a specific domain that is where I take the allowed ...
0
votes
1answer
90 views

Some doubts about predicate calculus

I am studying the predicate calculus in First Order Logic and I have some doubt about this argument. In my book I find that a formula in the predicate calculus is built from Literals constructed ...
0
votes
2answers
606 views

what is the diffrence between a term , constant and variable in first order logic languages ?

in the text , the author says that the language contains parenthises , sentintial connectives and n-place functions , n-place predicates , equality sign = , terms , constans and variables i have two ...
4
votes
2answers
237 views

a good text for a first course in mathematical logic

in last two months , i asked many people about good text for first mathematical logic . after that a chose some text , first order mathematical logic , angelo magrais , it is ok but the text uses ...
0
votes
1answer
69 views

what is the difference between formula and the abbrevation of a formula?

there is a problem which is asking me to determine whether a string is a formula or an abbrevation of a formula but i don't know the diffrence of formula and the abbrevation of a formula i know ...
1
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2answers
321 views

what is the definition of an interpretation of first order theory $T$ ? what is a model for $T$?

what is the definition of an interpretation of first order theory $T$ ? what is a model for $T$ ? can you give me the definition supported with some simple examples ? i read the definition in ...
-3
votes
1answer
111 views

what does two words F , G are initial mean ? with some examples .

what does two words F , G are initial mean ? with some examples . also there is a lemma says , for any formula f in F and any word w in W(A) , if w is initial segment of F , then o[w] >= c[w] ...
1
vote
2answers
49 views

if F , G are two formulas , h[f] is the height of the formula f ,then h[ G a F ] is less or equal to sup( h[F] , h[G] ) + 1

if F , G are two propostional formulas , h[f] is the height of the formula f , then h[ G a F ] is less or equal to sup( h[F] , h[G] ) + 1 , a is one of the connectives , my question is , what is sup ...