In this paper, we present the foltonl system, which converts first order logic fol sentences into natural language nl ones. Transcribing english to predicate logic wffs subjects to be learned. The first aspect is paraphrasing statements involving various nonstandard connec. Foe firstorder english is an artificial language whose syntactic and. When the modal depth of a formula is k, then the first order logic formula contains a chain of k transitions from the starting world.
The first step in the translation process is to determine what a wellformed proposition looks like. The translation of sentences in natural language nl into. Statements about similar objects and relations needs to be enumerated. We want to be able to say this in one single sentence. Examples for how to translate english sentences into firstorder logic.
A translation technique is presented which transforms a class of. For example, the ace reasoner is an automated theorem prover that can convert english text into firstorder logical predicates. Functional translation and secondorder frame properties. Do tools or libraries capable of translation an english sentence into first order logic exist. Quantification converts a propositional function into a proposition by binding a variable to a set of values from the universe of discourse. Examples for how to translate english sentences into first order logic if you would like to practice, there are some more problems in the exercises of chapter 8, e.
If you would like to practice, there are some more problems in the exercises of. It thus eliminates possibilities of misinterpretation of sentences. If you would like to practise, there are some more problems with sample solutions in nilsson, section 15. The operator ax should be read as everything is such that.
Translating english to propositional logic phil 57 section 3 san jose state university fall 2010. Firstorder logic propositional logic assumes the world contains facts that are true or false. If a user is active, at least one network link will be available. 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. Oct 07, 2010 translating english to propositional logic phil 57 section 3 san jose state university fall 2010 slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you would like to practise, there are some more problems with sample solutions in.
Relation between description logics and firstorder logic. Doing this in propositional logic would require to include statements about. In this handout i treat the notation of truthfunctional propositional logic and firstorder predicate logic as a language, and give guidance on translating from english into this foreign language. How to translate these sentences into first order predicate. Examples for how to translate english sentences into firstorder logic if you would like to practice, there are some more problems in the exercises of chapter 8, e. In the present chapter, we are interested chiefly in two aspects of paraphrase. Translation foe firstorder english is an artificial language whose syntactic and semantical rules are based on those of the uninterpreted firstorder language fol firstorder logic, as described in a separate handout. Cohen philosophy of language translation foe firstorder english is an artificial language whose syntactic and semantical rules are based on those of the uninterpreted firstorder language fol firstorder logic, as described in a separate handout. Everything is a hungry friend of mine and im not hungry. Translation of english sentences into first order logic.
The motivation comes from an intelligent tutoring system teaching. However, whenever i convert some sentences into fol, i get errors, i read many books and tutorials, do u have any tricks that can help me out, some examples where i makes errors. Pdf converting first order logic into natural language. Propositional and first order logic background knowledge. Finally, we will write some sentences in foe, along with their translations into. In this handout i treat the notation of truthfunctional propositional logic and first order predicate logic as a language, and give guidance on translating from english into this foreign language. The difference between fol and foe is that the nonlogical vocabulary of. An introduction to formal logic open textbook library.
First order logic, translation an english sentence. This assumption can make it awkward, or even impossible, to. In modal logic, standard translation is a way of transforming formulas of modal logic into formulas of firstorder logic which capture the meaning of the modal formulas. Let sx mean x is a skier, mx mean x is a mountain climber, and lx,y mean x likes y, where the domain of the first variable is hoofers club members, and the domain of the second variable is snow and rain. Let q, r, and srepresent you can ride the roller coaster. Propositional logic is a weak language hard to identify individuals e. Consequence there is no algorithm that decides whether a. Translation of first order formulas into ground formulas via a.
The second step is to specify a way to interpret what propositions say about the world. The modal depth of a formula also becomes apparent in the translation to first order logic. Hauskrecht limitations of propositional logic world we want to represent and reason about consists of a number of objects with variety of properties and relations among them propositional logic. Firstorder logic godels completeness theorem showed that a proof procedure exists but none was demonstrated until robinsons 1965 resolution algorithm. Language for each of the following formulas indicate.
As an exercise, figure out whether you could get essentially the same results by using a more direct translation i. Translate from english to firstorder logic mathematics. In many ways, learning how to translate into frstorder logic is like learning how to program. Remove universal quantification symbols by first moving them all to the left end and making the scope of each the entire sentence, and then just dropping the prefix part. Firstorder logic cs 2740 knowledge representation m. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading. It should be determined in advance whether you are using restricted quanti. Translating into logic is a skill that takes some practice to get used to, but once. Translating sentences into compound statements removes the ambiguity. How can this english sentence be translated into a logical expression. Subramani1 1lane department of computer science and electrical engineering west virginia university 30 january, 4 february, 6. Examples for how to translate english sentences into first order logic if you would like to practise, there are some more problems with sample solutions in nilsson, section 15. Translation using quantifiers and predicates youtube.
Translating english sentences to wff contents english sentences appearing in logical reasoning can be expressed as a wff. Guide to firstorder logic translations stanford university. Predicate logic is used for specifying properties that systems must satisfy. We can now translate the above english sentences into the following fol wffs. In last fridays lecture, we talked about how to translate statements from english into frstorder logic. In classical logic, firstorder existential quantifiers can be eas ily removed by. Every mail message larger than one megabyte will be compressed. Standard translation is defined inductively on the structure of the formula. The worlds are chained in the sense that these worlds are visited by going. Unfortunately there are hilbert axioms which do not have corresponding firstorder properties for the accessibility relation.
Examples for how to translate english sentences into firstorder. 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. Many description logics are decidable fragments of first order logic fol, also known as first order predicate calculus fopc, and many of twovariable logic or guarded logic, however, some description logics have more features than first order logic. It is also possible to convert natural language into first order logic using a discourse representation theory. What kinds of truth conditions would you get if you translated 6 literally. Predicate logic with questionanswer animations summary predicate logic first. You have to think though the logical structure of what it is you want to say. You cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old. Represents statements about the world without reflecting this.
In short, atomic formulas are mapped onto unary predicates and the objects in the firstorder language are the accessible worlds. Aug 24, 2017 i translate a few sentences into logic notation using predicates and quantifiers. Translation tips peter suber, philosophy department, earlham college. Translations in sentential logic 109 a only if b is paraphrased not a if not b in other words, the if stays put, and in particular continues to introduce the antecedent, but the only becomes two negations, one in front of the antecedent introduced by if, the other in front of the consequent. In some cases, there is not even any reasonable approximation in. Translation from natural language to first order logic. First order predicate logic limitation of propositional logic the facts. Translating into logic is a skill that takes some practice. First, recall that statements may be divided into simple statements and compound statements.
Exercises first order logic universit a di trento 17 march 2014 exercise 1. Firstorder logic assumes the world contains objects. Chapter 4 the world according to predicate logic overview at this stage of our course, you already know propositional logic, the system for reasoning with sentence. Examples for how to translate english sentences into firstorder logic if you would like to practise, there are some more problems with sample solutions in nilsson, section 15. Decide on predicates and domains left implicit here for the variables. Translating firstorder theories into logic programs ijcai. Transcription from english to predicate logic general principles of transcription in transcribing an english sentence into predicate logic, some general principles apply. First order logic formulas, called restricted formulas, into ground. Many description logics are decidable fragments of firstorder logic fol, also known as firstorder predicate calculus fopc, and many of twovariable logic or guarded logic, however, some description logics have more features than firstorder logic. Examples for how to translate english sentences into first. Paraphrase is translation from english into english, which is presumably easier than translating english into, say, japanese. Having trouble with a translation in firstorder logic.
Hauskrecht order of quantifiers the order of nested quantifiers matters if. For example, the ace reasoner is an automated theorem prover that can convert english text into first order logical predicates. In general, i omit logical issues, such as methods for making use of the expressions once translated. 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 a lot of fun. Whereas the latter are constructed from smaller statements using statement connec. Examples for how to translate english sentences into firstorder logic if you would like to practice. Order logic fol, predicate calculus not covered the language of quanti. Automatically converting natural language to firstorder logic.
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. An existentially quantified sentence is true in a model if it holds under. Nov 09, 2012 propositional logic is a weak language hard to identify individuals e. It is also possible to convert natural language into firstorder logic using a discourse representation theory. I translate a few sentences into logic notation using predicates and quantifiers. Translate an english sentence to first order logic. It implies that you are both hungry and not hungry. Examples for how to translate english sentences into first order logic if you would like to practice. An existentially quantified sentence is true in a model if it holds under any extended interpretation in which its variables are assigned to domain elements.