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Computational logic is the branch of logic and computer science that studies how to implement mathematical reasoning and logical formalisms using computers. This includes, for example, automatic theorem provers , which employ rules of inference to construct a proof step by step from a set of premises to the intended conclusion without human intervention. [ 169 ]
- Introduction
- Logical Sentences
- Logical Entailment
- Logical Proofs
- Symbolic Logic
- Automation
- Reading Guide
- Recap
- Exercises
Logic. It is one of the oldest intellectual disciplines in human history. It has been studied through the centuries, by Gottfried Leibniz, George Boole, Charles Babbage and Lady Lovelace, Russell and Whitehead, and others. And it is still a subject of active investigation today. We use Logic in just about everything we do. We use it in our professi...
For many, Logic is an esoteric subject. It is used primarily by mathematicians in proving complicated theorems in geometry or number theory. It is all about writing formal proofs to be published in scholarly papers that have little to do with everyday life. Nothing could be further from the truth. Consider the interpersonal relations of a small gro...
Once we know which world is correct, we can find that some sentences must be true even though they are not mentioned in the premises we are given. For example, in the first world we saw above, everybody likes somebody even though we are not told that fact explicitly. Unfortunately, things are not always so simple. Although logical sentences can som...
One way to check whether a set of sentences logically entails a conclusion is to examine the set of all worlds in which the given sentences are true. Unfortunately, determining logical entailment by checking all possible worlds is impractical in general. There are usually many, many possible worlds. Moreover, in some cases the number of possible wo...
So far, we have illustrated everything with sentences in English. While natural language works well in many circumstances, it is not without its problems. Natural language sentences can be complex; they can be ambiguous; and failing to understand the meaning of a sentence can lead to errors in reasoning. As an example of ambiguity, suppose I were t...
The existence of a formal language for representing information and the existence of a corresponding set of mechanical manipulation rules together have an important consequence, viz. the possibility of automated reasoningusing digital computers. The idea is simple. We use our formal representation to encode the premises of a problem as data structu...
Although Logic is a single field of study, there is more than one logic in this field. In the three main units of this book, we look at three different types of logic, each more sophisticated than the one before. Propositional Logic is the logic of propositions. Symbols in the language represent "conditions" in the world, and complex sentences in t...
Logic is the study of information encoded in the form of logical sentences. Each logical sentence divides the set of all possible world into two subsets - the set of worlds in which the sentence is true and the set of worlds in which the set of sentences is false. A set of premises logically entails a conclusion if and only if the conclusion is tru...
Exercise 1.1:Consider the state of the Sorority World depicted below. For each of the following sentences, say whether or not it is true in this state of the world. Exercise 1.2:Consider the state of the Sorority World depicted below. For each of the following sentences, say whether or not it is true in this state of the world. Exercise 1.3:Conside...
Mar 8, 2021 · According to Ole Hjortland, Timothy Williamson, Graham Priest, and others, anti-exceptionalism about logic is the view that logic “isn’t special”, but is continuous with the sciences. Logic is revisable, and its truths are neither analytic nor a priori. And logical theories are revised on the same grounds as scientific theories are. What isn’t special, we argue, is anti-exceptionalism ...
- Marcus Rossberg, Stewart Shapiro, Stewart Shapiro
- 2021
Sep 30, 2024 · philosophy of logic. logic, the study of correct reasoning, especially as it involves the drawing of inferences. This article discusses the basic elements and problems of contemporary logic and provides an overview of its different fields. For treatment of the historical development of logic, see logic, history of.
Philosophy of logic, the study, from a philosophical perspective, of the nature and types of logic, including problems in the field and the relation of logic to mathematics, computer science, the empirical sciences, and human disciplines such as linguistics, psychology, law, and education.
Sep 16, 2000 · Classical Logic. Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language has components that correspond to a part of a natural language like English or Greek. The deductive system is to capture, codify, or simply record arguments that are valid for the given ...
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Sep 3, 2023 · Logic, in its essence, is a tool—a lens through which we can view the world. As a science, it offers a framework for understanding the principles of correct reasoning. As an art, it champions the skillful application of these principles to navigate the complexities of human discourse and decision-making. Perhaps the beauty of logic lies in ...
