Questions tagged [logic]

Questions related to mathematical logic and its use in computer science

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Algorithm for automatic construction of natural deduction proofs

I was wondering if there exists any algorithm for automatic construction of nautral deduction proofs. I'm interested in propositional logic and first order logic. If there is no algoritm, can you ...
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Algorithm for deducing values

I have a group of logical conditions and need to deduce values that would NOT satisfy them. For example: City != New York && Location = Museum ...
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Did Wheeler really believe that physics was undecidable?

John Archibald Wheeler was a famous physicist It has been stated that he thought that there was a strong connection between undecidability and quantum physics This idea was given an early ...
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Substituting a term for a variable in a context

At this link you can read Nicola Gambino's slides on one way to approach the formal syntax of Martin-Löf dependent type theory. (They are concise and very readable.) On slide 10, he gives a standard ...
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Is it possible to do forward-chaining in Prolog?

Prolog (or any logic programming system) actually acts as SAT solver, that returns the valid values for the variables that are mentioned in the query. It can also be used as theorem prover if one does ...
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Logical inference as Markov decision process?

Are there efforts to consider forward or backward (theorem proving) logical inference process as Markov decision process in which the the action space is: 1) selection of the inference rule (e.g. from ...
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Prove propositional formula is a tautology [closed]

I need to show this formula is a theorem of propositional calculus. I tried assuming antecedent and proving consequent but didn't work for this proof. Do I need to show it is equivalent to true? How ...
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Examples for Partial Combinatory Algebras

I am currently working on my Bachelor thesis about Turing Categories (see Introduction to Turing Categories [1]). In this context I got some questions regarding Partial Combinatory Algebras (PCAs), ...
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Why does the unbounded $\mu$ operator preserve effective computability?

Let $f$ be a partial function from $\mathbb{N}^{p+1}$ to $\mathbb{N}$. The partial function $(x_1,...,x_p)\mapsto \mu y[f(x_1,...,x_p,y)=0]$ is defined in the following way: If there exists at least ...
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propositional Modal logic filtration definition

Hello I have a slightly unusual question which relates to a definition of filtration structure. The following is my current state of the definition: $ \mathcal{M} = (W, R, L) $, W is a set of worlds, ...
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How to prove a LTL formula correct in a specific model?

I have been learning Verification by model checking recently and I get the following question: $Whether\ the\ LTL\ formula\ M, q_3\ \models (X\ \lnot a) \rightarrow (F\ G\ \lnot a)\ is\ established\ ...
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What is the minimun type of logical system that recognizes if a formalized sentence is a well-formed formula thus reducible to the boolean value?

The formula, in the old way of using it, can contain symbols in order and a mixture that does not meet the criteria of correctness (i.e. arbitrary symbols do not form a well-formed formula (WFF) and ...
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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 ...
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Translation of diagnosis problem to SAT

I have the following diagnosis problem: h(A): z1 = not(in1) h(D): z2 = not(in2) h(B): z3 = z1 or z2 h(C): out1 = not(z3) h(E): out2 = not(z3) This is an image of the system: I have an observation ...
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1answer
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List of all possible reasoning tasks - satisfiability and theorem proving only?

What is the exhaustive list of reasoning tasks? As far as I can understand, then any logical reasoning reduces to 2 tasks only: 1) satisfiability problem (finding the assignment of the variables) and ...
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how do we demonstrate using Boolean algebra that these NAND and NOR gate combinations are XOR gates

How do we demonstrate using Boolean algebra that these NAND and NOR gate combinations are XOR gates?
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Two questions on MSO

First question : Is the following formula a valid MSO formula? $\theta(S, r) = \exists (e_1, t_1), ... ,(e_h, t_h) \bigwedge\limits_{(e_i, e_j) \in \rho(S,r)} \mathcal{R}((e_i, t_i), (e_j, t_j)...
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MSO (Monadic second-order logic) Logic On Words

Let L be a language over $\Sigma = \{a,b,c\}$ that contains all words, where the length $|w|_b$ (number of all b's) has remainder 1 if divided by 3. MSO logic over words are definded as follow: I ...
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What is the connection between the logic and the logic programming?

As I understand, then logic (i.e. particular theory of logic with some theory's axioms and some possible assignments of the variables) describes some specific world (in the non-modal case) or some set ...
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How to draw an LTS based on the parallel process “|” in CCS Milner's logic?

I'm trying to provide a Hennessy-Milner logic formula for CCS expressions that are not (strongly) bisimilar. An example with a sketch: For each of the following CCS expressions, decide whether ...
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Boolean expression for sum bit of full adder

The Boolean expression I find on the internet for the sum bit of a full adder is A xor B xor Cin. Does't this expression exclude the A=1,B=1,Cin=1 situation? When that happens, the sum bit is also 1, ...
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Law as a computer science problem?

For a long time, computer scientists and logicians have noticed that law (statutes, contracts, adjudication, etc), has some similarity with formal logic and programming languages, and have approached ...
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What is this weird gate?

This came from a picture of something that I'm supposed to make, and I can't find it in the program I'm supposed to use (LogicWorks). It looks like it 'not's only one of its inputs, but that doesn't ...
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The barbers paradox first order logic formalization

I tried to look on the site and while I found some similar questions, I did not find the first order logic formalization of the following sentence (the basic barber's paradox), so I wanted to ask if I ...
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The difference between dynamic logic and temporal logic

To find the difference, I'd just encountered with assertions below about temporal logic in Wikipedia: another variant of modal logic sharing many common features with dynamic logic, differs from ...
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Modeling equality in an ILP

Lets say we have integer variables $a \in\mathbb{Z}^n$ and $M \in\{0,1\}^{n\times L}$. I am promised $a_i \leq L$, for some fixed constant $L$. I want to model the constraint $$M_{i,j} \iff (a_i=j)$...
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37 views

Logic of multiple variables in ILP

Is there a better way to represent an AND of $n$ variables together other than creating $O(n)$ new variables and constraints?
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Efficient method for generating the smoothing function

The smoothing function of a boolean function with respect to one of its variables is the disjunction of its cofactors. For example given a Boolean function F(a,b,c) the cofactors with respect to a are ...
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Basic second-order logic example contains a mistake?

I'm reading the following course on second-order logic, by Péter Mekis : http://phil.elte.hu/mekis/sol.pdf . The course seems excellent, but I'm stuck on one of his first examples for showing the ...
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How do we know $\neg \neg LEM$ isn't provable in MLTT?

I've been trying (fruitlessly) to prove something which I now know is not provable. Take the following definitions: $$LEM \equiv \prod_{A : Type} \neg A \vee A$$ $$DNE \equiv \prod_{A : Type} \neg \...
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Are the two LTL properties $GF(\psi_1 \land F\psi_2 )$ and $GF(\psi_2 \land F\psi_1 )$ equivalent?

Is $GF(\psi_1 \land F\psi_2 )$ equivalent to the property $GF(\psi_2 \land F\psi_1 )$? Attempt: In the first property each state must eventually see $\psi_1$ and $\psi_2$, in the second property as ...
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Algorithm to find possible variables in multiple connected equations

I am new here. I am trying to come up with an algorithm that can give me the unknown values in the following equation. ...
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Handling $AND$ and $OR$ cases in MILP?

Suppose I want to have an integer program for handling the cases $x_1>1\wedge x_2>1\wedge x_3>1\wedge\dots\wedge x_n>1\iff\delta=1$ $x_1>1\vee x_2>1\vee x_3>1\vee\dots\vee x_n&...
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Hoare triple: Loop invariant and correctness

The following Hoare triple in which variable a is an array of integers, and len, max, i, n, j and m are integer-valued variables. Provide a loop invariant (using predicate logic) suitable for proving ...
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Hoare triple: Loop invariant and partial correctness

Below there is Hoare triple in which variable $a$ is an array of integers, $len$, $x, i$ are integer-valued variables, and $r$ is a Boolean-valued variable. I have to provide a loop invariant (using ...
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kPDA handling multiple epsilon transtions

I'm assigned to build a kPDA with 2 stacks that handles {w#w, where w is a string of (0,1)*}. I understand the # delineates the two strings, but I'm unsure of the logic when popping off stacks with ...
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What are the other language models of computation similar to lambda calculus?

I hope this question makes sense, but I was wondering if there are other models of computation similar to lambda calculus that you can use to build up axiomatic mathematical and logical fundamentals ...
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(Generally) How to specify asynchronous action with side effects using logic equations

Say you have this function call sequence: function all() { fn1() fn2() fn3() } And say that fn2 was asynchronous and ...
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Why do ¬, ∀ and ∃ have the same precedence?

I thought the order of precedence of operators and quantifiers was arbitrary, but I don't really understand why those three have the same "strength" in relation to other operators (e.g., ¬ will have ...
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How do I get the NAND gate configuration for full adder from the logic table?

I'm self-studying, but I've gotten stuck already. If I'm given the logic table for a full-adder or any two-output table, how do I figure out the NAND-gate configuration, preferably methodically? ...
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Validity of □(P→ Q) → (◊P → ◊Q) in linear temporal logic

How can I prove that $\Box(P\rightarrow Q)\rightarrow (\Diamond P\rightarrow\Diamond Q)$ is valid in linear temporal logic (LTL)?
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Can we ignore the postcondition in the Hoare conditional rule when there is a return statement?

I'm proving the correctness of naive string matching using Hoare logic. I have the following pseudocode: ...
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Negation of the semantics of the Until operator in LTL

I have been looking at the Until operator and the release operator and when introduced to the release operator it was suggested that it is equivalent to: $\phi R \psi \equiv \neg(\neg\phi U \neg \psi)...
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Turing Machine where branches are resolved via arbitrary operator

Alternating Turing Machines output Boolean values and combine the values returned by branches via the any/all operators. Is ...
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If a NAND gate is universal, why you don't have NAND OISCs

If a NAND gate can be used to construct all other of the basic logic gates, then I'm wondering why you don't/can't have a purely NAND-based One Instruction Set Computer (OISC). All the OISC single ...
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Can we see all of mathematics as an attempt to simplify computations?

This is a rather strong claim, and therefore likely to be incorrect, but hear me out. Firstly, when I talk of “computations”, I mean this in a broader sense than normally used, because I am including ...
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Examples of logic gates using non-standard models

These are the only ones I have been able to find online: Pulley Logic Gates Marble adding machine MARBLE COMPUTER LOGICAL AND GATE I would like to find some more discrete models like these (as ...
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LTL to Büchi automaton, deterministic?

I know it is possible to convert LTL formulas to Büchi automatons. But is it possible to convert a LTL formula to a deterministic Büchi automaton? Are there formulas that can't be converted to a ...
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How to understand the notion of boolean query via Immerman's definition

A query is any mapping $I:STRUC[\sigma] \to STRUC[\tau]$ that is polynomially bounded. A boolean query is a map $I_b: STRUC[\sigma] \to \{0,1\}$. A boolean query can also be thought as the susbset: $...