Example exercises and answers for predicate logic inference (+ FOL in general)

In summary, the author is struggling with first order predicate logic and is having difficulty applying the rules of inference from the textbook. He is looking for a source of help to learn the material and has tried several books but has hit a wall.
  • #1
vasra
5
0
I'm battling with first order predicate logic (no identity, no extensions) and currently esp. inference using the so called "natural reasoning" rules for inference.

Now, the textbook we use, is very ambiguously defined, even I have spotted several 'errors' in it, the lecturer even more.

This makes learning formal systems quite hard for me, as I don't always grasp things, if they are not accurately defined.

Also, the examples for doing inference are terse. There are only a few and they are the simplest of forms. Most of what I would consider 'recurring patterns' of partial inference are not covered. Absolutely no heuristics are given, even the simple ones that I've been able to come up with myself.

Hence, I've been doing progressively more difficult inferences for my course now for four weeks.

But now I've hit a wall.

I have tried, re-tried, slept a day, re-tried, started over, taken a fresh approach, chunked the problem to smaller parts, etc.

No dice, can't get this weeks exercises solved. I could barely muster last weeks after two days of trying, but I did them. Not these.

I'm not yet willing to accept that this stuff is too difficult for me to learn by myself and that I should just give up.

But I suspect there are things I've misunderstood or not properly understood, hence my difficulty in applying the rules of inference.

Now my question:

Does anybody know of any source, free or for-pay, for learning logic (incl. FOPL esp. doing inferences and the proofs for major theorems) that has plenty of self-study examples including full step-by-step answers and even explanations.

I'm not (too) afraid of formalism, but I need the fluffy natural language explanations too.

I guess I'm just slow (being dyslexic doesn't help), but I'm not yet willing to give up.

It's just that I think I've hit a wall with what I can extract from our very thin course book and I need an additional source.

Anyone?

All pointers appreciates.

As background, I'm an adult student getting back to math & phys after 15 year break and really starting over from basics. Some uni basics level linear algebra, computability and discrete maths + extensive high school maths, but that's it and it's 15 years ago. So no book is _too_ simple for me :)

PS Naturally I've done very extensive google/msn/yahoo searches but I've have found quite little of what is really useful for doing inferences. Quite a lot of definitions using various notations styles, but examples have been really simple, and absolutely no heuristics, no answers to difficult questions and very few examples altogether.
 
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  • #2
Gathering answers I've got.

The following books were recommended:

A Friendly Introduction to Mathematical Logic, Christopher C. Leary, out of print
[sorry, not allowed to posts urls yet]

I'll post more for others' benefit, if I get them.
 
  • #3
have you tried peter suber's site?
 
  • #4
I will, thanks.
 

1. What is predicate logic inference?

Predicate logic inference, also known as first-order logic inference, is a method used in mathematical and scientific reasoning to draw conclusions from given premises and rules. It involves using logical rules to determine the truth or falsity of statements.

2. How does predicate logic inference differ from propositional logic?

Predicate logic inference allows for the use of quantifiers, such as "for all" and "there exists", which propositional logic does not. This allows for more complex and precise reasoning about mathematical and scientific statements.

3. What are some common exercises for practicing predicate logic inference?

Some common exercises for practicing predicate logic inference include converting natural language statements into symbolic logic, using truth tables to evaluate arguments, and constructing proofs using inference rules.

4. Can you provide an example of a predicate logic inference problem and its solution?

Example problem: Given the premises "All cats are mammals" and "Fluffy is a cat", use predicate logic inference to determine if the conclusion "Fluffy is a mammal" is valid.

Solution: Using the universal instantiation rule for "for all" quantifiers, we can infer that "Fluffy is a mammal" is true since "Fluffy" is a specific instance of the general category "cat". Therefore, the conclusion is valid.

5. How can understanding predicate logic inference be useful in scientific research?

Understanding predicate logic inference can be useful in scientific research as it allows for rigorous and systematic reasoning about complex statements and arguments. It can also help in identifying and correcting errors in scientific theories and experiments.

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