Slides of the diagrams and tables in the book in both pdf and latex can be down. Modelsstructures that interpret the symbols of a formal systemare often. A structure that satisfies all the axioms of the formal system is known as a. Part of their charm is the contrast between the typical. An introduction to logical spreadsheets michael kassoff1 and andre valente2. The first part deals with the logical aspects of logic programming and tries to provide. Logical ai involves representing knowledge of an agents world, its goals and the current situation by sentences in logic. The logician customarily uses a symbolic notation to express such.
Constable computer science department, cornell university. There are many formal systems of logic, each with their own set of inference rules. Mathematical logic, important in formal methods of software development and in arti. What are the practical applications of formal logic, outside. Metatem does not formally distinguish between events and fluents, and does not. A logic program is represented by formulas axioms a set of sentences in logical form, expressing facts and deductions about a. The close link between logic as a formal system and computerbased theorem proving is proving to be very useful especially where there are a large number of cases following certain patterns. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The basis of fca is a formal context that associates attributes to objects. Predicates can be combined together using logical operators. There have been many attempts to extend prolog to be closer to the ideal of logic programming. Logic programming cmu school of computer science carnegie. The previous examples show that a lazy narrowing strategy is more difficult to.
Although he studied logic as a basis for functional programming rather than logic programming, his ideas are more fundamental and therefore equally applicable in both paradigms. Specifically, we are interested in horn logical semanticsdenotational semantics expressed in horn logicof programming languages. You mentioned programming as a professional programmer, i find having studied logic useful not just at the level of using logical operators such as and, or or not in programming statements, but also in terms of the overall. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. Without su cient automation of formal reasoning methods these cannot be done for huge industry scale programs. In the examples, in figure 3 and elsewhere in the paper, we use variables in the. If your roommate picked up the book and thumbed through. Programming in logic without logic programming arxiv. Logic and abstraction, verification and falsification jangeorg smaus. The transition systems studied in my work are logic and functional programs on the. Logic information systems lis use logic in a uniform way to describe their contents, to query it, to navigate through it, to analyze it, and to update it. Since a computer program is simply a formal description of a calculation, it can be. We are trying to make language mechanisms which behave like thought.
Written in a clear, precise and userfriendly style, logic as a tool. Propositional logic is defined over a domain of discourse of allowed predicate symbols, p. Chess is a formal system, with configuration being chess po sitions. Logic programmer logic programming concept lattice logical formula formal context. Logic information systems for logic programmers springerlink. Pdf logic information systems for logic programmers. While the most basic operation in logic programming is unification, in constraint logic programming, unification is replaced by constraint propagation, of which unification is a special case.
An introduction to formal logic open textbook library. An introduction to formal logic textbook equity open. Logical systems formalize reasoning and are similar to programming. Formal systems, logic and semantics daniel richardson, department of computer science, university of bath. Formal logic, the abstract study of propositions, statements, or assertively used sentences and of deductive arguments. The agent decides what to do by inferring that a certain action or course of action is appropriate to achieve the goals.
Formal logic softwareanalysisprogramming language s. We are trying to catch some aspects of the action of intelligence within formal systems. Types in logic, mathematics and programming robert l. A formal system is a set of data structures together with a set of transfor mations which act on them. Scott, in programming language pragmatics third edition, 2009. Formal logic is used for specifying and verifying computer systems and sometimes for representing knowledge in arti. What are the practical applications of formal logic.
However, logic programming systems need not necessarily be based on resolulion. An introduction to logic programming through prolog. An introduction to program logic and the formal development of software. The user of a logic program states a theorem, or goal, and the language implementation attempts to find a collection of axioms and inference steps including choices of. Applications for simplification and manipulation of logical systems symbolically.
It shows how to encode information in the form of logical sentences. Prolog programming in logic is a representative logic language. Languages, algorithms, procedures, calculi and metalogic arxiv. Libraries to facilitate programming in relation to formal logic systems you will need one of the commonly available unzip utilities, such as pkunzip or winzip or tar, depending upon your system environment. The first programmable logic controller plc was developed by a group of engineers at general motors in 1968, when the company were looking for an alternative to replace complex relay control systems. Moreover, there are several different types of formal proof systems. They can be nonclausal systems with many inference rules 11, 41, 42. Review of concepts from formal logic 1 basic logical operations.
A guide to formal logical reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classical logic as a tool for doing correct reasoning. A descriptive term for logic programming and expert systems is automated reasoning systems. Programs are written in the language of some logic. Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. Yet, it is possible for someone besides a logic student to read this book. The new control system had to meet the following requirements. The close link between logic as a formal system and computerbased theorem proving is proving to be very useful especially where there are a. The journal of logic, language and information explores the foundations of natural, formal, and programming languages, as well as the different forms of human and mechanized inference. Logic programming systems allow the programmer to state a collection of axioms from which theorems can be proven. The discipline abstracts from the content of these elements the structures or logical forms that they embody. Logic and logic programming department of computer science. People have probably always invented and puzzled over formal systems, as described above. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading.
Many systems for reasoning by computer, including theorem provers, program veri. Formal system, also called logistic system, in logic and mathematics, abstract, theoretical organization of terms and implicit relationships that is used as a tool for the analysis of the concept of deduction. Logic is the study of how truth is defined, and how we prove that certain statements are true or false. Rules are written as logical clauses with a head and a body. Formal system, in logic and mathematics, abstract, theoretical organization of terms and implicit relationships that is used as a tool for the analysis of the concept of deduction. It covers i basic approaches to logic, including proof theory and especially. Theory, practice and applications qian wang, michael nichols, and gopal gupta in this project we study the formal semantics of programming languages and their applications. Logic programming is a computer programming paradigm in which program statements express facts and rules about problems within a system of formal logic. Horn clause logic and resolution underlie the very widespread use of logic programming, while algorithms for automated theorem proving have long been of interest to computer scientists for both. This account only discusses logic programming systems based on resolution and concentrates particularly on the prolog systems which are currently available. This course is an introduction to logic from a computational perspective. We will learn how to apply these tools to certify that programs behave as expected.
Execution of a logic program is a theorem proving process. Later in the course we will more formally establish soundness and non deterministic. A generalization of logic programming called constraint logic programming allows for sophis. Since logic programming computation is proof search, to study logic programming means to study proofs. Principles of programming languages computer science. Unfortunately, the state of art of these processes is such that they can be done only for small programs. Lloyds foundations of logic programming 1987 provides a theoretical explanation of the formal semantics of prolog and related languages.
Formal logic, symbolic logic and mathematical logic tend to exist mainly in academia, but the methods of formal logic have inspired informal logic, which can be used anywhere. We characterize brie y a large number of concepts that have arisen in research in logical ai. Formal proof systems of logic define a finite set of inference rules that reflect baby inferences. According to modeltheoretic interpretation, the semantics of a logical system describe whether a wellformed formula is satisfied by a given structure. Theory and implementation programmable controllers an industrial text company publication atlanta georgia usa second edition l. Simple programming program changes without system intervention. Logic is also of primary importance in expert systems in which the inference engine reasons from facts to conclusions. Deductive reasoning can be weakened so that it can be modelled by formal systems. Deontic logic is the field of logic that is concerned with obligation, permission, and related concepts. Logic information systems lis use logic in a uniform way to describe their. A third use of logic is as a data model for programming languages and systems, such as the language prolog. Preface this book is an introduction to logic for students of contemporary philosophy.
At its core, mathematical logic deals with mathematical concepts expressed using formal logical systems. Axiom systems sequent systems natural deduction systems other. Important examples are formal grammars for generating formal lan guages, formal proof systems in predicate logic, the lambda calculus which formalises symbolic computation, and populations of autonomous agents. This has led to a profound analysis of the structure of language, which has proved to be of importance for many philosophical discussions.
An introduction to logical spreadsheets stanford logic group. Facts are expressed similar to rules, but without a body. Formal logic is a powerful and universal representation formalism in computer science, and also in this book we cannot completely get around it. The design and study of such formal systems is the primary motivation of the. Programming is concerned with the logical aspects of program organi. Metalogic can in turn be roughly divided into two parts. Logic programming is a programming paradigm based on formal logic. Studying logic programming is a good introduction to mathematical logic, because the logic behind logic programming is simple, and allows results. It covers the logical, linguistic, and informationtheoretic parts of the cognitive sciences. In formal logic, a formal system also called a logical calculus citation needed consists of a formal language and a set of inference rules, used to derive to conclude an expression from one or more other premises that are antecedently supposed axioms or derived theorems.
A logical system or, for short, a logic, is a formal system together with its semantics disputed discuss. These logical systems provide the immediate subject matter for metalogical investigation. A logical system specifically designed for program verification. Modelsstructures that interpret the symbols of a formal systemare often used in conjunction with formal systems. Logic knowledge can also be represented by the symbols of logic, which is the study of the rules of exact reasoning. Logic in this form has also been used to specify the meanings of some programming languages, notably pascal. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems. Logic programming is a way of writing computer programs using languages that are based on formal logic.
Review of concepts from formal logic 1 basic logical. I have chosen these examples of desired behaviour because they are the most. Logical information systems lis use logic in a uniform way to describe their contents, to query it. The argument forms of the first two socrates examples can be abstracted to. System language, which combines reactive rules and logic programs. It offers a systematic and precise exposition of classical logic with many examples and. Pdf an introduction to program logic and the formal development. Logic programming an overview sciencedirect topics. Logic programming definition of logic programming by the. These systems, though they differ in many details, share the common property of considering only expressions in a fixed formal language. Programmable logic controllers, basic level textbook. A generalization of logic programming called constraint logic programming allows for sophisticated numerical and symbolic constraintsolving.
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