# semantics

## Sentential Logic: 10 Tutorials

Topic
Logical System
###### 7/6/12

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.

## Easy Deriver [Sentential and Predicate Logic—Bergmann Syntax]

Topic
Logical System
###### 7/5/12

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.

## Tutorial 23: The semantics of relations

Topic
Logical System

### The Tutorial

The semantics of relations proceeds in much the way one would expect-- the new item that has to be taken account of is the order of the terms (because, for example, Tab is not at all the same thing as Tba -- Arthur being taller than Beryl is not the same as Beryl being taller than Arthur).

Interpretation 1

Universe= {a,b}
F={a}

## Help with the semantics of free variables

Topic

12/25/06

### Introduction to Free Variables

This video illustrates use of the downloadable application (and the symbol ∧ for 'and' and (∀x) for the universal quantifier, some systems use (x) for this). But, what the film depicts and explains is equally good if you happen to be using the web pages applets (or different symbols for 'and' and the universal quantifier).

Your browser does not support html5 video.

## Tutorial 17: The semantics of quantifiers

Topic
Logical System

Under revision 2013

### The Tutorial

We will certainly wish to discuss the truth and falsity of formulas with quantifiers in them.

Interpretation 1

Universe= {a,b}
F={a}

## Tutorial 14: Some Terminology for the Semantics of Predicate Logic

Topic
Logical System

### The Tutorial

A few concepts are needed give a simple portrayal of the truth and falsity of predicate logic formulas.

There is the notion of an Interpretation which consists of a Universe together with an account of how the various symbols in the predicate logic formulas apply in this Universe.

There should be a Universe, which is the collection of the objects that the formulas is about. We write, for example,

Universe = {a,b,c}

Topic
Logical System

## Predicate Logic: 15 Tutorials

Topic
Logical System

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.

Topic
Logical System

Topic
Logical System