# Questions tagged [propositional-logic]

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### Is there a correspondence of steps between DPLL and sequent-calculus?

Is there a correspondence between the steps in using DPLL to find out that a formula in propositional logic is unsatisfiable and using sequent calculus to prove that its negation is valid? And given ...
47 views

### A Quine–McCluskey variant for conjunctive normal formal?

There is the Quine–McCluskey algorithm for finding a minimal expression of a boolean expression in dis-junctive normal form. Would applying DeMorgan's rule to the minimal DNF result in the minimal CNF?...
67 views

### Why Modus ponens works with Horn clauses and Generalized Modus ponens requires definite clauses?

I am reading the Artificial Intelligence: A Modern Approach book and in the chapters about logic i noticed that in propositional logic the Modus ponens inference rule (used by the forward and backward ...
39 views

### Is there a formula that is not logical equivalent to any Horn clause?

There are of course formulas that can't be transformed into a Horn clause but is it possible to construct an equivalent Horn clause that is true under the same interpretation?
56 views

### What is the difference between the situation calculus and the propositional logic of context?

I have been reading a lot of papers by John McCarthy lately. As early as 1963, he developed the situation calculus, but then starting in 1987, he developed what came to be known as the propositional ...
63 views

### How to minimize large DNF formula into deeper but smaller formula?

I want to minimize DNF formula which has ~200k products combined into a sum. The depth of that formula is 2 - first level is the OR, and second level is AND for all conjunctions. I have tried using ...
67 views

### What is the definition of the property of Canonicity for a logic?

I'm trying to understand "A Systematic Approach to Canonicity in the Classical Sequent Calculus" by Kaustuv Chaudhuri, Stefan Hetzl, Dale Miller. The article discusses a property called "canonicity" ...
68 views

### Refutation of pigeonhole using resolution

I am trying to find a way to refute the pigeonhole formula using resolution. Lets assume that $x_{ij}$ is true if $i^{th}$ pigeon is in $j^{th}$ hole. Thus, with $n$ holes and $n+1$ pigeons, the ...
258 views

### Propositional logic in an SMA* algorithm

I'm trying to implement an SMA* graph search algorithm that I found in a paper here(Rong Zhou, Eric A. Hansen: Memory-Bounded A* Graph Search. FLAIRS-02 Proceedings 203-209) and I would like to ...
34 views

### What does the structure ($S_t^x P$) in this Existantial Instantiation imply, Skolemization?

The sheet of equivalences given to us in class provides the two equivalences \begin{array}{|c|c|c|} \hline \text{Universal Instantiation} & \forall x ~ P(x) \implies {S_t}^x P & \exists y ~ \...
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### Efficiently decidable logics

So propositional logic (PL) is efficiently (in P) decidable because I can convert formulas to an equisatisifiable CNF-formula, negate and convert (efficiently, by De Morgans laws) to DNF. I can then ...
17 views

### What could be the bound of the number of elements of a models of a given first order sentence?

Sorry for the weird title. The Problem: Consider the first-order logic sentence φ≡∃s∃t∃u∀v∀w∀x∀yψ(s,t,u,v,w,x,y) where ψ(s,t,u,v,w,x,y,) is a quantifier-free first-order logic formula using ...
39 views

### How to write negation of an 'AND' statement in logic

Suppose the given proposition is: "Zach blocks emails and texts from Jennifer" Where, P implies "Zach blocks emails from Jennifer". Q implies "Zach blocks texts from Jennifer". So it's P AND Q in ...
48 views

### What are necessity and sufficiency?

I was reading deadlock topic from Operating Systems book by Stallings. It states four pre requisites for deadlock: Mutual exclusion No preemption Hold and wait Circular wait It then have following ...
92 views

### How to construct an NFA Ai for the given Regular property P1 and P2?

Let AP = {a; b; c}. Consider the following regular safety properties: (a) P1: If a becomes valid, afterwards b stays valid ad infinitum or until c holds. (b) P2: Between two ...
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### Resolution with multiple variables

Resolution allows to generate new clauses for an existing set of clauses. In many cases, the rule is simple: ...
Let $\varphi$ be a boolean formula in 3-CNF form (conjunctive normal form with three literals at most per clause). I want to convert it to an equivalent boolean formula that uses only NOR gates with ...