symbolization

Example only

Tutorial 16 Symbolization using the quantifiers.

2013

Skill to be acquired in this tutorial:

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

The Tutorial

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).

11/30/06

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

Symbolization using the Universal Quantifier (of non relational English)

2013

Tutorial 22 Symbolizing Relations.

The Tutorial

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.

Tutorial 16 Symbolization using the quantifiers.

2013

Skill to be acquired in this tutorial:

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

The Tutorial

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).

10 Software

In predicate logic, many different styles of expression in English get cast into the same 'property-is-had-by-entity' form. For example,

2013

Skills to be acquired in this tutorial:

To start learning how to symbolize propositions using predicate logic.

The Tutorial:

There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,

Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.

There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,

Beryl is a philosopher.
All philosophers are wise.
Therefore
Beryl is wise.

1/24/06

eg Lander or Suber

The problem or issue here lies with the truth table for the conditional (or material implication) ⊃

There is the idea of setting up a code or convention or dictionary between atomic propositions and capital letters.

There are compound propositions, each of which has a main connective which connects its components.

There are five propositional logical connectives:

'∼' which translates back to 'it is not the case that...'

'∧' which translates back to '... and ...'

'∨' which translates back to '... or ...'

'³' which translates back to 'if... then ...'

'≡' which translates back to '... if and only if ...'

8/29/06

Tutorial 2 Example: How Experts Symbolize