## Help with Tutorial 2

8/29/06

### Tutorial 2 Example: How Experts Symbolize

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Logical System

8/29/06

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Logical System

9/1/12

Symbolizing compound sentences. Learning about logical connectives, and the notion of the main connective. Recognizing different constructions in English which have the same underlying logical form. Paraphrasing the English into a standard form.

It is the next step in learning how to symbolize. Main connectives are very important-- they are central to symbolization, they are central to the semantics, and they are central to derivations.

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Logical System

To become familiar with the notions of argument, valid, invalid, premise, and conclusion. To learn how to symbolize atomic sentences.

Bergmann[2004] *The Logic Book* Chapter 1

The main role of logic is to assess arguments-- to say whether an individual argument is valid or whether it is invalid. In logic, arguments are taken to consist of two components--premises, and a conclusion.

For example,

Logical System

Indicative sentences in a natural language, English, for instance, are either true or false. For example, 'There are 35 State Governors in the U.S.A.' is an indicative sentence (which happens to be false). Such sentences express statements or propositions. Not all pieces of language express propositions. For example, the question 'What day is it today?' is not either true or false (although reasonable answers to it will be either true or false); again, the greeting 'Have a nice day!' is not either true or false.

Logical System

Welcome!

These web pages provide an introduction to logic to the level of Propositional and Predicate Calculus.

The focus of the program is on arguments and the question of whether they are valid. Arguments have the form <list of premises> ∴<conclusion>. An argument is valid if and only if it is not possible for all its premises to be true and its conclusion false at one and the same time; an argument which is not valid is invalid.

Topic

Logical System

2013

To learn how to use the Universal and Existential Quantifiers in symbolizing propositions.

In Predicate Logic there are two new logical connectives, the* Universal Quantifier* (∀x) and the *Existential Quantifier* (∃x). These are used for symbolizing certain English constructions (they also have their own rules of inference and their own semantics, which we will learn about later).

Topic

Logical System

11/30/06

[The core of this is from Leblanc and Wisdom [1972] p.117 and f.]

Topic

Logical System

2013

Thus far we have considered only 'monadic' predicates-- our atomic formulas consist of a predicate followed by only one term-- for example, Fx. But in English we regularly encounter dyadic predicates or relations. For example, 'Arthur is taller than Bert' cannot be symbolized with the tools we have used so far; what is needed is a relation to represent '...is taller than ...' Txy, say, and then the proposition would be symbolized Tab.

Topic

Logical System

2013

To learn how to use the Universal and Existential Quantifiers in symbolizing propositions.

In Predicate Logic there are two new logical connectives, the* Universal Quantifier* (∀x) and the *Existential Quantifier* (∃x). These are used for symbolizing certain English constructions (they also have their own rules of inference and their own semantics, which we will learn about later).