We know from Church's Theorem that L_1 is Turing-undecidable. And we now know from Olmsted's theorem...

We know from Church's Theorem that L_1 is Turing-undecidable. And we now know from Olmsted's theorem that L_0 is Turing-decidable. AI of today, and specifically AI as it relates to the Web, particularly the Semantic Web, is often connected to formal logics "between" L_0 and L_1. Let us define the logic L_1^cdot as first-order logic but with no function symbols allowed, and having relation symbols that are all unary. Your question is: Is theoremhood for L_1^cdot Turing-decidable, or does Church's Theorem apply?

Solutions

Expert Solution

Solution:

It is given that is Turing-unecidable and is Turing decidable from Olmsted's theorem.

= first-order logic but with no function symbols allowed, and having relation symbols that are all unary.

First of all it needs to be understood what a Turing decidable language is -

A language L that is decided by a Turing machine means if there is a Turing machine M such that M halts and accepts on any input w ∈ L, and M halts and rejects on input input w L; i.e., looping cannot happen.

This means the language is closed under union, intersection and other set operations but is not as it is not turing decidable.

Since is turing undecidable, it is confirmed that any set operation on can't be Turing Decidable.

So, the answer is big NO that = first-order logic is not Turing Decidable.

Moreover, Church's theorem can be applied to find whether it is Turing Decidable or not.

venereology answered 1 month ago

Next > < Previous

Related Solutions

Which of the following problems about Turing machines are solvable, and which are undecidable? Explain your...

Which of the following problems about Turing machines are solvable, and which are undecidable? Explain your answers carefully. (a) To determine, given a Turing machine M, a state q, and a string w, whether M ever reaches state q when started with input w from its initial state. (b) To determine, given a Turing machine M and a symbol a, whether M ever writes the symbol a when started with the empty tape.

Show that the following problem i undecidable: Input: A Turing machine M. Output: Yes if M...

Show that the following problem i undecidable: Input: A Turing machine M. Output: Yes if M eventually halts when started on a blank tape, no otherwise Input: A Turing machine M and a tape symbol a. Output: Yes if M eventually writes a when started on an blank tape, no otherwise. Input: A Turing machine M. Output: Yes if M ever writes a nonblank symbol when started on a blank tape, No otherwise. Input: A Turing machine M and a...

Plato is concerned with the question of how we now what we know. What are the...

Plato is concerned with the question of how we now what we know. What are the fundamental issues that he is raising?

1. what is genome sequencing? what do we now know about the human genome from sequencing...

1. what is genome sequencing? what do we now know about the human genome from sequencing it? 2. explain different applications of genomics. What are SNPs is and how are they useful? 3. what are the uses of biotechnology in medicine?

Now that we know a bit more about epidemiologic curves and the important steps in an...

Now that we know a bit more about epidemiologic curves and the important steps in an outbreak investigation, let's see how this is playing out with COVID-19. 1. You've probably heard public health officials say that we need to "flatten the curve". What does this statement mean and why is it so important? 2. Discuss one method public health officials have implemented to flatten the COVID-19 curve. Do you think this method is effective? Explain. 3. Will the nation-wide Black...

OK, we all know by now that security practices are important to the organization. You may...

OK, we all know by now that security practices are important to the organization. You may have security champions who are ready to tout the merits of having a security conscious organization. They know your organization, the business processes and the technology used within the company. They often will guard against weak attitudes when it comes to security, and will offer solutions to protect vital data. As our culture has ever increasing access to information, social engineering will still be...

"We now know that the core molecular cause of Parkinson's disease and Huntington's disease resembles that...

"We now know that the core molecular cause of Parkinson's disease and Huntington's disease resembles that of several other neurodegenerative disorders: Creutzfeld-Jakob disease, Alzheimer's disease, frontotemporal dementia, chronic traumatic encephalopathy (the progressive brain degeneration seen in people who have suffered repeated concussions), and the genetic form of amyotrophic lateral sclerosis (ALS or Lou Gehrig's disease). All of these diseases result from abnormally folded proteins that form clumps in the brain, becoming toxic and eventually killing neurons. In 1982, Stanley Pruisner...

What do we know now about the link between human diseases and gene mutations.

based on Marx and Smith and Meiksins Wood, describe/summarize how the system we now know as...

based on Marx and Smith and Meiksins Wood, describe/summarize how the system we now know as capitalism emerged out of the feudal order in Europe. two paragraphs each 1) Structural differences: What are the structural differences between feudal society and the capitalist system that eventually replaced? What do the systems have in common? What are the differences? 2) Dynamic transformation: Why did the institutions of the feudal system (described in a) change ? What social processes produced these changes? What...

We want to save $120,000 now and $150,000 one year from now for possible replacement of...

We want to save $120,000 now and $150,000 one year from now for possible replacement of the old computer. If the replacement will occur at the end of 5 years from now. How much will we have in the account, given the interest rate is 10% per year? Your answer should include the cash flow diagram, the related factors, such as (P/F,i%,n), and the final answer. The calculation should be done manually and also by EXCEL. You may insert the...

Subjects