Propositional and first order logic computer science. The material presented here is not a direct component of the course but is offered to you as an incentive and a support to understand and master the concepts and exercises presented during the course. We will sometimes distinguish a special binary relation symbol. This new logic affords us much greater expressive power. This node contains two installments of the notes describing basic results on first order logic. Firstorder logicalso known as predicate logic, quantificational logic, and first order predicate. In last fridays lecture, we talked about how to translate statements from english into frst order logic. Propositional logic propositions are interpreted as true or false infer truth of new propositions first order logic contains predicates, quantifiers and variables e. Practice in 1st order predicate logic with answers. Propositional and first order logic background knowledge profs. It is part of the metalanguage rather than the language. The british mathematician and philosopher george boole 18151864 is the man who made logic. Course notes on first order logic this node contains one installment of the course notes for mits graduate course on the foundations of artificial intelligence.
In these notes we will study rst order languages almost exclusively. Note that that implication direction his switch from the previous. These lecture notes discuss the syntax, semantics, and pragmatics of the language of. The examples in the last section can be encoded in fol 8xrichx 9yownsx. Translating into logic is a skill that takes some practice to get used to, but once you get the hang of it, its actually not too bad and honestly it can be. General rst order theories will be investigated in chapter 5.
Chapter 4 introduces students to three areas of logic with broad application in. Birzeit university, palestine, 2015 mjarrar2015, 2 watch this lecture and download the slides acknowledgement. Firstorder logic whereas propositional logic assumes the world contains facts, firstorder logic like natural language assumes the world contains objects. In firstorder logic the atomic formulas are predicates that assert a relationship among.
This chapter is dedicated to another type of logic, called predicate logic. Subramani1 1lane department of computer science and electrical engineering. Inference in firstorder logic department of computer. Logic is more than a science, its a language, and if youre going to use the language of logic, you need to know the grammar, which includes operators, identities, equivalences, and quantifiers for both sentential and quantifier logic. Symbolic logic notes on the interpretation of firstorder logic notes for symbolic logic fall 2005 john n. Propositional and first order logic propositional logic first order logic basic concepts propositional logic is the simplest logic illustrates basic ideas usingpropositions p 1, snow is whyte p 2, otday it is raining p 3, this automated reasoning course is boring p i is an atom or atomic formula each p i can be either true or false but never both. Firstorder logic fol is a logic that gives us the ability to quantify over objects. Artificial intelligence practice questions on propositional and first order logic 1. No further parentheses are needed here, and according to the syntax on. Inference in firstorder logic 12 march 2019 forward chaining algorithm 29 function folfca sk kb, returns a substitution or false. Firstorder logic propositional logic only deals with facts, statements that may or may not be true of the world, e. Firstorder logic godels completeness theorem showed that a proof procedure exists but none was demonstrated until robinsons 1965 resolution algorithm. Because it gives us a tool for doing resolution in the first order case.
Note that all of these methods are generalizations of their. Gate cs topic wise preparation notes geeksforgeeks. This document is highly rated by computer science engineering cse students and. Apr 08, 2020 propositional and first order logic computer science engineering cse notes edurev is made by best teachers of computer science engineering cse. We can now define formulas using formulas and predicate symbols.
Fd is a function from dn to d for every function symbol f of arity n. Einstein in the previous chapter, we studied propositional logic. Syntax we shall now introduce a generalisation of propositional logic called. Dmitri gallow 1 spring, 2015, new york university 1 these notes were designed to accompany the online software for hurleysaconciseintroductiontologic. Special care is given to explaining prolog in the language of first order logic and for motivating the resolution proof technique within herbrands model theory.
Propositional and first order logic background knowledge. First order logic propositional logic assumes the world contains facts that are true or false. Terms and formulas firstorder logic has two different kinds of syntactic. First order logic is a generalization of propositional logic and is described in the next two chapters. General logic firstorder logic university of wisconsin. The above examples can also be done using truth tables. Note that if c is a 0ary function symbol, then c is a term. But that means todays subject matter is firstorder logic, which is extending propositional logic so that we can talk about things. Base if tis a constant symbol or an individual variable, then tis a term. Most theoremproving programs are organized using the resolution method for. Lecture notes on mathematical logic vladimir lifschitz january 16, 2009 these notes provide an elementary, but mathematically solid, introduction to propositional and. You will often see fol called rstorder predicate logic or rstorder predicate calculus. If there is gas in the tank and the fuel line is okay, then there is gas in the engine.
John, 3, predicate symbols refer to particular relations in the model. This page contains gate cs preparation notes tutorials on mathematics, digital logic, computer organization and architecture, programming and data structures, algorithms, theory of computation, compiler design, operating systems, database management systems dbms, and computer networks listed according to the gate cs 2020 syllabus. Note that there is no special category for the syntax of logic languages, it is. Cdm firstorder logic cmu school of computer science. This type of system is called firstorder logic fol or predicate logic. Quantifiers, start on inference and proofs pdf, pptx note.
Lecture 10 software engineering 2 first order logic. Lecture notes on discrete mathematics birzeit university. Notes on first order logic notes for phil370 eric pacuit november 30, 2012 1 the language of first order logic the language of predicate logic is constructed from a number of di erent pieces of syntax. Introduction to articial intelligence firstorder logic. More answers for practice in logic and hw 1 this is an expanded version showing additional right and wrong answers.
And, if youre studying the subject, exam tips can come in. These lecture notes discuss the syntax, semantics, and pragmatics of the language of firstorder logic, also called predicate logic. If there is gas in the engine and a good spark, the engine runs. To properly write primex asa firstorder formula we need to replace that. A language lconsists of a set l fof function symbols, a set l rof relation symbols disjoint from l f, and a function arity. Propositional logic and its applications pdf, docx lecture 2. Semantics of firstorder logic a little more formally. First order logic assumes the world contains objects. Philosophera scholara x, kingx greedy x evil x variables range over individuals domain of discourse second order logic. Also relevant is melvin fitting, first order logic and automated theorem proving springer, 1996 the following book provides a different perspective on modal logic, and it develops propositional logic carefully. Inf5390ai05 first order logic constants, predicates, functions and terms constant symbols refer to specific objects in the world. In this section we present the basics of classical. Note that in the definition of primex we have used the previous abbreviation.
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