Firstorder logic godels completeness theorem showed that a proof procedure exists but none was demonstrated until robinsons 1965 resolution algorithm. We introduced resolution as a refutation procedure for prop. A brute force algorithm to answer a query to a logical agent that has a knowledge base of propositional logic. Resolution refutation an overview sciencedirect topics. Binary resolution is the only inference rule that you need to prove that a rst order sentence follows from a kb. The first step is to write each axiom as a wellformed formula in firstorder predicate calculus. First order logic godels completeness theorem showed that a proof procedure exists but none was demonstrated until robinsons 1965 resolution algorithm. Resolution principle for first order logic resolution for fol completeness of resolution examples of resolution deletion strategy resolution principle for fol brief recap. Artificial intelligence indian institute of technology. Propositional form once sentences are in clausal form, we can apply the resolution inference process.
The symbol d5hv denotes the inference mechanism of first order resolution without paramodulation. Resolution refutation procedure aka resolution procedure. Its more complicated in the first order case, as well see. Cvetan dunchev 1, alexander leitsch, mikheil rukhaia, and daniel weller2 1 institute of computer languages e185, 2 institute of discrete math. But first well take an initial look at robinsons resolution method of inference. By iteratively applying the resolution rule, it is possible to tell whether a propositional formula is satisfiable. So, although many reasoning problems can be formulated as problems of resolution refutation, the method is intractable for very large problems. Resolution is used, if there are various statements are given, and we need to prove a conclusion of those statements. It says if you have a formula alpha or phi and another formula not psi or beta, and you can unify phi and psi with unifier theta, then youre allowed to conclude alpha or beta with the substitution theta applied to it. Scribd is the worlds largest social reading and publishing site. Resolution in propositional and firstorder logic umbc csee. First order logic resolution first order logic logical. Firstorder predicate logic, which offers a much richer language for. Plresolution and firstorder logic firstorder logic.
Proof by resolution refutation in rst order logic cannot, in general, decide whether a. Propositional logic propositional resolution propositional theorem proving unification today were going to talk about resolution, which is a proof strategy. First order logic resolution with variables clausal form lecture 8 2. But there is another way, in which we first rewrite the ifthen wff as b v a. In general, a set s of clauses may have more than one refutation.
The resolution principle for first order logic resolution for fol completeness of resolution examples of resolution deletion strategy. Logic and deduction first order logic inference in first order logic resolution refutation proofs introduction to planning graphplan and satplan satplan reasoning under uncertainty bayesian networks. Weve been doing firstorder logic and thinking about how to do proofs. 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. Scan p and q lefttoright and find the first corresponding terms where p and q disagree. Propositional and first order logic background knowledge. Resolution is sound and complete for fopc but can be very inef. Resolution in predicate logic resolution method is used to test unsatisfiability of a set s of clauses in predicate logic. Firstorder logic syntax, semantics, resolution computer science. With this ordering and selection function the refutation proceeds strictly deterministinally in this example. Logic and resolution institute for computing and information. Formulas of propositional logic are defined by the following grammar in. Any first order logic sentence can be converted to a.
It is an extension of resolution method for propositional logic. Inference in firstorder logic department of computer. Resolve them together, performing all required unifications c. Hustadt2 1 the university of manchester, uk, renate. Generally, proof search will still be non deterministic but. To prove b from a and a b, we can use modus ponens. In other words, iteratively applying the resolution rule in a suitable way allows for telling whether a propositional formula is satisfiable and for proving that a firstorder formula is unsatisfiable. May never halt resolution is semidecidable puts burder on user to be decidable and tractable thus far. So resolution refutation for propositional logic is a complete proof procedure.
The conclusion can be proved using resolution as shown below. Inference and resolution university of california, san diego. Inference in firstorder logic philipp koehn 12 march 2019 philipp koehn arti. It will actually take two lectures to get all the way through this. Last time we looked at how to do resolution in the propositional case, and we looked at how to do unification that is, essentially matching of terms, figuring out. Resolution is a theorem proving technique that proceeds by building refutation proofs, i. First order logic has been used in modelling planning, expertise, natural language processing, etc. Resolution for first order logic meghdad ghari institute for research in fundamental sciences ipm school of mathematicsisfahan branch logic group. We know how to match literals containing variables using. How does a resolution algorithm work for propositional logic. Resolution refutation given a knowledge base kb collection of true sentences a proposition p we wish to prove that p is true. The variables can be quantified talk about all of them or some of them without naming them specifically. Resolution inference an overview sciencedirect topics. It was invented by a mathematician john alan robinson in the year 1965.
In this paper we give an overview of results for modal logic which can be shown using techniques and methods from. We can prove it by resolution refutation by negating the sentence and trying to. Propositional resolution is a powerful rule of inference for propositional logic. Convert all sentences to cnf negate the desired conclusion. Refutation when resolution is used to prove inconsistency, it is also called refutation. Firstorder logic chapters 8 9 firstorder logic fol or fopc syntax. The resolution principle for first order logic profs. Computational properties of resolution and firstorder logic.
The resolution rule for firstorder logic is simply a lifted version of the propositional rule. Convert english sentence into folfirst order logic in hindi artificial intelligence series duration. Resolution can resolve two clauses if they contain complementary literals, which are assumed to be standardized apart so that they share no variables. A clausal resolution calculus for monodie first order temporal logic based on that described in section 9. Firstorder logic syntax, semantics, resolution ruzica piskac yale university ruzica. If resolvent is the empty clause, a contradiction has been found i. First order logic resolution with variables clausal form weve been doing first order logic and thinking about how to do proofs.
Inference and resolution introduction to artificial intelligence csece 348. In this section, we describe how to extend resolution to. Extracting information from resolution proof trees 29 substitution instances of s. Propositional resolution resolution is a refutation procedure used to check if a formula in clausal form is unsatis. The calculus is not particularly practical as the resolution rules require the complex combination of clauses. Based on proof by contradiction and usually called resolution refutation. First order logic resolution free download as powerpoint presentation. If we succeed in step 4, we have proved the conclusion. Firstorder logic firstorder logic fol models the world in terms of objects, which are things with individual identities properties of objects that distinguish them from other objects relations that hold among sets of objects functions, which are a subset of. Resolution in firstorder logic with tutorial, introduction, history of artificial. Resolution 14a 14 young won lim 81514 resolution resolution is a rule of inference leading to a refutation theoremproving technique for sentences in propositional logic and first order logic.
Inference in firstorder logic 2 first order deduction. In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theoremproving technique for sentences in propositional logic and firstorder logic. Refutation when resolution is used to prove inconsistency, it is called refutation. A resolution refutation of s is a resolution proof of empty clause. Basic steps for proving a conclusion s given premises premise1, premisen all expressed in fol. Also, there is a recursive operation which yields both the terms t and a propositional calculus proof of the disjunction from the conjunction, given the original proofp. 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 resolution based inference fol refutation complete for general kb. Resolution inference rule is sound and complete refutation complete for the propositional logic and cnf generalized resolution rule is sound and refutation complete for the first order logic and cnf wo equalities if unsatisfiable the resolution. Resolution refutation in fol first order predicate logic lecture 5.
1110 251 187 579 1307 397 528 79 255 1221 492 1336 971 1151 1333 1477 230 535 1008 307 267 288 7 292 628 1081 1207 903 1237 1335 1431 622 252 1283 1410