author: aman
Blog II - Part II - Day 09
Hope you people got an intuition about the Formal Methods & Verifications in the latest blog. However, if you feel like having a query, that possibly I can solve, please drop an email to aman0902pandey@gmail.com.
This blog will cover the explanation about what is known as, First-Order Logic. Plus in the very next micro-blog, most importantly what was my approach, with Dr Pramod, at IIT Kanpur. And the applications of Formal Methods in it. This one will only roam around the First-Order-Logics....
Lets get in...
In this micro-blog
- Formal Methods
- Formal Verification
- First Order Logic
- Information Flow and Vulnerability
- ..... will keep adding
First Order Logic
Well, the first order logic has several philosophical theories. I'll stay with the one most understood by me.
The FOL, are the extensions of the logics, to what we call as Propositional Logics. The only difference is that the FOL also covers the predicates and quantifications.
Quite confusing, right!?
Lets break them into smaller parts.
- Propositional Logics: These logics only covers the "propositional arguments", which are the statements which are logical(i.e. they can be true or false). The propositional formulas, are written by using certain symbols.
*remember the same thing you've learned in your school times....
here, p,q,r,s are the predicates, for eg.(p -> people who are quarantined for 6 days), and the complete notation in the above image is the propositional formula.
Predicates: can be simply defined as a few functions/operations with have either of the 2 values: 0 or 1. This is very important when we will be discussing the satisfiability in checking the systems. That will eventually lead to an understanding of how these are applied to the real world problems, and security, as we'll be discussing in case of blockchain.
Quantifications: simply stands for "quantifying" things or better to say objects. The FOLs also try to give no. to the objects. and that's it.
So, the FOLs are the way to represent a few conditions, with the use of propositional symbols, predicates, functions & Symbols, quantifiers. These representations lead to some "understanding", and this understanding is called as "interpretations".
These interpretations are the whole lot which governs the mathematical science behind using these logics while describing a secure systems.
Propositional logics are also known as zeroth-order-logic as it is extending the First-Order-Logic
Don't lose your heart, if you were not able to understand somethings, or anything at all. A few examples, and applications have got your back.
Keep Up....