Guide to firstorder logic translations stanford university. Firstorder logic propositional logic only deals with facts, statements that may or may not be true of the world, e. Inference in first order logic santa clara university. Learn the definitions of trees, and graphs learn about state and problem spaces learn about andor trees and goals explore different methods and rules of inference learn the characteristics of firstorder predicate logic and logic systems. Inference in first order logic chapter 9 outline reducing first order inference to propositional inference unification generalized modus ponens forward chaining backward chaining resolution universal instantiation ui every instantiation of a universally quantified sentence is entailed by it. While defining inference, we mean to define effective procedures for answering questions in fopl. If a sentence is entailed in the original 1st order logic, then it is entailed in a. The first in the phrase firstorder logic is to distinguish this form of logic from stronger logics, such as secondorder or weak secondorder logic, where certain extralogical notions set or natural number are taken as given in advance. Theres a new kind of syntactic element called a term. This assumption can make it awkward, or even impossible, to. Artificial intelligence practice questions on propositional and firstorder logic 1. If there is gas in the tank and the fuel line is okay, then there is gas in the engine.
Firstorder logic uses quantified variables over nonlogical objects and allows the use of sentences that contain variables, so that rather than propositions such as socrates is a man. Thursday, october 28, 2010 inclass closed book what does it cover. Propositional logic propositional resolution propositional theorem proving unification today were going to talk about resolution, which is a proof strategy. The country nono, an enemy of america, has some missiles, and all of its missiles were sold to it by colonel west, who is american. We encounter logic in natural language with words and phrases such as if then, implies, on. Sound and complete for firstorder definite clauses proof similar to propositional proof. Inference in firstorder logic firstorder deduction. Inference in first order logic fol and unification. Requires kb to be in form of firstorder definite clauses backwardchaining works backwards from a query to try to construct a proof can suffer from repeated states and incompleteness useful for querydriven inference resolutionbased inference fol refutationcomplete for general kb. Firstorder logic, secondorder logic, and completeness. If something is intelligent, it has common sense deep blue does not have common sense.
First order logic fol is exactly what is sometimes been thought of as good oldfashioned ai gofai and what was the central target of critique on ai research coming from other. Its a logic like propositional logic, but somewhat richer and more complex. First, well look at it in the propositional case, then in the first order case. Note that there is a controversial point regarding this, because you could simply decide to make relations and functions be your objects and then second order logic would be first order logic. Propositional logic use the definition of entailment directly. In practice, can be much faster polynomialtime inference procedure exists when kb is expressed as horn clauses. Thus the first in first order logic describes the type of objects that can be quantified. Guide to expressing facts in a firstorder language ernest davis september 28, 2015 there is no cookbook method for taking a fact expressed in natural language or any other form and expressing it in. Translating into logic is a skill that takes some practice to get used to, but once. Please help with translation of english to first order logic.
In this, we can infer any sentence by substituting a ground term a term without variables for the variables. Nov 09, 2012 propositional logic is a weak language hard to identify individuals e. Substitution is a fundamental operation performed on terms and formulas. Inference appoaches in fol forwardchaining uses gmp to add new atomic sentences useful for systems that make inferences as information streams in requires kb to be in form of firstorder definite clauses backwardchaining works backwards from a query to try to construct a proof. Inference rules forward chaining backward chaining resolution. You have to think though the logical structure of what it is you want to say. Declarative language before building system before there can be learning, reasoning, planning, explanation. Information and translations of firstorder logic in the most comprehensive dictionary definitions resource on the web. Outline n reducing first order inference to propositional inference n generalized modus ponens n forward chaining n backward chaining n resolution 2. 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. Jul 20, 2015 introduction to inference in fol and unification no unification algorithm is offered, but the idea is discussed. But the most paper are always writing about the term superposition calculus. Introduction to artificial intelligence sharif university of technology spring 2017 artificial intelligence.
Firstorder logic does not only use predicate and terms for making atomic sentences but also uses another way, which is equality in fol. If we succeed in step 4, we have proved the conclusion. Unlike first order logic, for which only one semantics is studied, there are several possible semantics for second order logic. Guide to expressing facts in a first order language ernest davis september 28, 2015 there is no cookbook method for taking a fact expressed in natural language or any other form and expressing it in. Inference methods in first order logic mustafa jarrar.
In all interpretations in which sentences in the kb are true, is also true. Inference in first order logic fol and unification youtube. Propositional and first order logic background knowledge. Basic steps for proving a conclusion s given premises premise1, premisen all expressed in fol. First order logic inference problem lecture 4 duration. Inference in firstorder logic chapter 9 outline reducing first order inference to propositional inference unification generalized modus ponens forward chaining backward chaining resolution universal instantiation ui every instantiation of a universally quantified sentence is entailed by it. Inference in firstorder logic colorado state university.
Reducing firstorder inference to propositional inference. Polynomialtime inference procedure exists when kb is expressed as horn clauses. Inference in firstorder logic philipp koehn october 2015 philipp koehn arti. Andintroduction, andelimination, or introduction, negation elimination additional inference rules are needed for sentences with quantifiers and variables must involve variable substitutions. Forward chainingbackward chainingresolution refutation. Thus, inference in first order logic can be achieved using. A modern approach, 3rd edition, chapter 9 soleymani. Pdf partial instantiation methods for inference in first. We use the term boolean valuation to mean any assignment of truth values to all formulas which satisfies the usual truthtable conditions for the logical connectives. Reducing firstorder inference to propositional inference unification generalized modus ponens. Inference in first order logic we may inference in fol by mapping fol sentences into propositions, and apply the inference methods of propositional logic. Firstorder logic lets us talk about things in the world. Predicate logic in propositional logic, each possible atomic fact requires a separate unique propositional symbol.
Our technique for proving this result originated in the adlerimmerman games, even though later it turned out that the. Inference in first order logic chapter 9 chapter 9 1. Proof procedure is exponential in n, the number of symbols. And the term, as well see when we do the semantics, is a name for a thing. Its an expression that somehow names a thing in the world. Methods of inference free download as powerpoint presentation. Models the completed open branch of the tableaux gives a model of kb. Introduction to articial intelligence firstorder logic. Resolution in firstorder logic university of washington. All material covered by the end of lecture today homework 7. Introduction to articial intelligence firstorder logic logic, deduction, knowledge representation bernhard beckert universit. Fol inference first order inference can be done by converting kb to propositional logic and using propositional inference using modus ponens, etc.
Introduction to inference in fol and unification no unification algorithm is offered, but the idea is discussed. The story so far 2 propositional logic subset of propositional logic. Pdf lecture 11 inference in first order logic hai v. We begin with preliminary material on trees necessary for the tableau method, and then treat the basic syntactic and semantic fundamentals of propositional logic. Firstorder logic fol is built around the above 3 elements. Inference appoaches in fol forwardchaining uses gmp to add new atomic sentences useful for systems that make inferences as information streams in requires kb to be in form of firstorder definite clauses backwardchaining works backwards from a query to try to construct a proof can suffer from repeated states and incompleteness.
Socrates, father, etc, which are often referred to by letters p, q, r etc. Before answering the question about firstorder logic, it is best to describe propositional logic and then describe how firstorder logic differs. The succinctness of firstorder logic on linear orders 3 result behind both parts of the theorem is that a 3variable. Well spend the first half of the lecture doing the same thing we did with propositional logic and going over syntax and semantics, and the second half practicing with the logic and, in particular, with. Dm18 first order logic learn to write statements duration. If resolvent is the empty clause, a contradiction has been found i. Translation from natural language to first order logic. Inference in first order logic russell and norvig chapter 9. Resolve them together, performing all required unifications c. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic. Firstorder logic godels completeness theorem showed that a proof procedure exists but none was demonstrated until robinsons 1965 resolution algorithm. Inference in firstorder logic northern arizona university.
Propositional logic is a weak language hard to identify individuals e. Propositional logic propositional logic consists of a set of atomic propositional symbols e. 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. Truth in firstorder logic sentences are true with respect to a model and an interpretation model contains objects domain elements and relations among them interpretation specifies referents for constant symbols objects predicate symbols relations function symbols functional relations. Unify is a linear time algorithm that returns the most general unifier mgu, i. 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. Outlinereducing rst order inference to propositional inference. Logic programming identify problem assemble information tea break encode information in kb ordinary programming. Smullyan is a wellknown logician and inventor of mathematical and logical puzzles. What is the difference between predicate logic, first order. It means that x have only two factors first is 1 and second is x itself. First order logic formalizes fundamental mathematical concepts expressive turingcomplete not too expressive not axiomatizable. It will actually take two lectures to get all the way through this. Learn the definitions of trees, and graphs learn about state and problem spaces learn about andor trees and goals explore different methods and rules of inference learn the characteristics of first order predicate logic and logic systems.
Firstorder logic propositional logic assumes the world contains facts that are true or false. Similarly, second order logic recognizes as formally valid certain inferences that are not fovalid. Propositional logic assumes that there are facts that either. It occurs in all inference systems in first order logic.
Inference in first order logic is used to deduce new facts or sentences from existing sentences. If there is gas in the engine and a good spark, the engine runs. But that means todays subject matter is firstorder logic, which is extending propositional logic so that we can talk about things. Change all statements in the knowledge base to propositions propositionalization with functions. Outlinereducing rst order inference to propositional inference uni cationgeneralized modus ponensforward and backward chaining logic programmingresolution chapter 9 2. Pdf application of firstorder logic in knowledge based systems. The big difference between propositional logic and first order logic is that we can talk about things, and so theres a new kind of syntactic element. Firstorder logic also known as predicate logic, quantificational logic, and first order predicate calculusis a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. Propositional logic from the viewpoint of analytic tableaux. Aristotelian forms, since they were first described. New methods for computing inferences in first order logic article pdf available in annals of operations research 439 september 1995 with 14 reads how we measure reads. Pdf new methods for computing inferences in first order. Firstorder logic assumes the world contains objects. In general, there is not a unique minimum length substitution list, but unify returns one of those of minimum length.
For this, we can use equality symbols which specify that the two terms refer to the same object. Outline reducing first order inference to propositional inference. Inference in first order logic cs 580 001 spring 2018 amarda shehu department of computer science george mason university, fairfax, va, usa april 11, 2018 amarda shehu 580 1. Firstorder logic firstorder predicate calculus 2 propositional vs. Inference in first order logic 2 first order deduction want to be able to draw logically sound conclusions from a knowledgebase expressed in. Practice in 1st order predicate logic with answers. If there are n people and m locations, representing the fact that some person moved from one location to another requires nm2 separate symbols.
Before understanding the fol inference rule, lets understand some basic terminologies used in fol. Reduction to propositional inference propositionalization. Hauskrecht logical inference in fol logical inference problem. The most commonly employed semantics for second order and higher order logic is known as full semantics. Inference in firstorder logic tutorial and example. For example, there is no way in fol to say that a and b have some property in common. Given a knowledge base kb a set of sentences and a sentence, does the kb semantically entail. A method to represent first order predicate logic horn clause logic by a dataflow network is presented. As a result, second order logic has much more expressive power than fol does. The law says that it is a crime for an american to sell weapons to hostile nations. This chapter discusses the formulas that are certain finite strings of symbols. In this book he has written a stimulating and challenging exposition of first order logic that will be welcomed by logicians, mathematicians, and anyone interested in the field. Firstorder logic is capable of expressing facts about some or all objects in the universe. Partial instantiation methods for inference in first order logic.