Propositional and first order logic pdf

Firstorder logic syntax objects are an important part of firstorder logic. This document is highly rated by computer science engineering cse students and has been viewed 20468 times. While propositional logic deals with simple declarative propositions, firstorder logic additionally covers predicates and quantification a predicate takes an entity or entities in the domain of discourse as input while outputs are either true or false. Propositional logic propositions are interpreted as true or false infer truth of new propositions first order logic contains predicates, quantifiers and variables e. Objects, which are things with individual identities. 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. First order predicate logic limitation of propositional logic the facts. Firstorder logic formalizes fundamental mathematical concepts expressive turingcomplete not too expressive not axiomatizable. First, well look at it in the propositional case, then in the firstorder case. Firstorder predicate logic also called just firstorder logic or predicate logic is a much more expressive logic that extends propositional logic in. While it has uses, propositional logic is not powerful enough to formalize most mathematical discourse. Introduction to articial intelligence firstorder logic.

In logic, a logical connective also called a logical operator, sentential connective, or sentential operator is a symbol or word used to connect two or more sentences of either a formal or a natural language in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective. If a proposition is true, then we say its truth value is true, and if a proposition is false, we say its truth value is false. The story so far 2 propositional logic subset of propositional logic. Introduction to articial intelligence firstorder logic logic, deduction, knowledge representation bernhard beckert universit. It is, frankly, quite unprofessional for the organising body to give as the syllabus mathematical logic. It is part of the metalanguage rather than the language. The emergence of firstorder logic stanford encyclopedia. Propositional logic, truth tables, and predicate logic. An introduction to the metatheory of standard first order logic. This assumption can make it awkward, or even impossible, to. A set of formulas is unsatis able i there is some nite subset of that is unsatis able.

The compactness theorem is often used in its contrapositive form. Propositional logic is a weak language hard to identify individuals e. A language lconsists of a set l fof function symbols, a set l rof relation symbols disjoint from l f, and a function arity. The theorem is true for both rst order logic and propositional logic. Predicate logic in propositional logic, each possible atomic fact requires a separate unique propositional symbol. Propositional and first order logic computer science. Firstorder logic assumes the world contains objects. Im assuming this is the indian state test graduate aptitude test in engineering 2014 for computer science and information technology. Fol is sufficiently expressive to represent the natural language statements in a concise way. Propositional and firstorder logic linkedin slideshare. May 15, 2020 propositional and first order logic computer science engineering cse notes edurev is made by best teachers of computer science engineering cse. For anybody schooled in modern logic, firstorder logic can seem an entirely natural object of study, and its discovery inevitable. Some statements cannot be expressed in propositional logic, such as. But that means todays subject matter is firstorder logic, which is extending propositional logic.

If p and q are propositions, then so are notp, p and q, p or q, p implies q, and p iff q. Propositional logic propositional resolution propositional theorem proving unification today were going to talk about resolution, which is a proof strategy. Consider the two sentences socrates is a philosopher and plato is a philosopher. Objects constants, variables, function calls appear. We will sometimes distinguish a special binary relation symbol. Pdf first order logic download full pdf book download. Properties of objects that distinguish them from other. Propositional logic is the simple foundation and fine for many ai problems. Semantics simplifying expressions practice using the equivalences we just established, simplify the following.

It works with atomic state ments that are either true or false. Here we have an opportunity to replace some sentences in firstorder logic with sentences in the propositional calculus. First order logic fol is much more express ive as a knowledge representation. If there are n people and m locations, representing the fact that some person moved from one location to another. Firstorder logic is also known as predicate logic or firstorder predicate logic.

Use the truth tables method to determine whether the formula. Sentences of our logic that have the same form as tautologies of the propositional logic we can still call tautologies. Cs 2710 foundations of ai administration second makeup lecture. A proposition or statement is a sentence which is either true or false. Propositional logic from the viewpoint of analytic tableaux.

Overview propositional logic is the most basic kind of logic we will examine. Firstorder logic is another way of knowledge representation in artificial intelligence. Propositional logic and firstorder logic mathematics. This work makes available to readers without specialized training in mathematics complete proofs of the fundamental metatheorems of standard i. The firstorder logic of proofs is not recursively enumerable arte mov yavorskaya, 2001. Summary of first order logic a concise introduction. The proof for rst order logic is outside the scope of this course, but we will give the proof for propositional logic. Predicate logic can express these statements and make inferences on them.

The logic book by merrie bergmann, et al, used to be used to teach propositional logic and firstorder predicate logic to philosophy undergraduates at university college london ucl and at the university of oxford. Firstorder logic propositional logic assumes the world contains facts that are true or false. But that means todays subject matter is firstorder logic, which is extending propositional logic so that we can talk about things. We begin with preliminary material on trees necessary for the tableau method, and then treat the basic syntactic and semantic fundamentals of propositional logic. Propositional and first order logic background knowledge profs. A proposition is a statement that is either true or false. At the end of the last lecture, i talked about doing deduction and propositional logic.

However, there are some sentences of the first order logic that must be true but that do not have the form of tautologies of the propositional logic. Firstorder logic in order to use the compactness theorem, and in fact, even to state it, we must rst develop the logical language to which it applies. The arithmetical provability semantics for the logic of proofs lp naturally generalizes to a firstorder version with conventional quantifiers, and to a version with quantifiers over proofs. However, an object by itself cannot be a firstorder logic sentence. Propositional logic attempts to make precise the relationships that certain connectives like not, and, or,andif then are used to express in english. The meaning of these combined propositions is given using a truth table. Notes on propositional logic and first order logic logica a torino. Firstorder logic 1 need for more than propositional logic in normal speaking we could use logic to say something like. Firstorder logic in artificial intelligence javatpoint. Subramani1 1lane department of computer science and electrical engineering. It will actually take two lectures to get all the way through this.