on 25-Apr-2018 (Wed)

Verbs ending in -cer add a cedilla to the c before the letters a or o in order to retain the soft c sound. avancer to advance nous avanc¸ ons

Verbs ending in -ger add an e after the g before the letters a and o in order to maintain the soft g sound. changer to change nous changeons

Verbs which have -é- in the penultimate syllable of the infinitive change -é- to -è- in all forms except the nous and vous forms.

compléter: je complète; tu complètes; il, elle, on complète; nous complétons; vous complétez; ils, elles complètent

In some verbs which contain -e- in the next to the last syllable of the infinitive, the -e- changes to -e ` - in all forms except the nous and vous forms. Study the following. lever je le ` ve tu le ` ves il, elle, on le ` ve nous levons vous levez ils, elles le ` vent

In other verbs with -e- in the infinitive, the final consonant is doubled in all but the nous and vous forms.

jeter: je jette; tu jettes; il, elle, on jette; nous jetons; vous jetez; ils, elles jettent

Verbs whose infinitive ends in -oyer, -uyer and -ayer change -y- to -i- in all but the nous and vous forms.

nettoyer: je nettoie; tu nettoies; il, elle, on nettoie; nous nettoyons; vous nettoyez; ils, elles nettoient

Verbs whose infinitive ends in -ir add -is, -is, -it, -issons, -issez, -issent to the stem.

finir: je finis; tu finis; il, elle, on finit; nous finissons; vous finissez; ils, elles finissent

Verbs whose infinitive ends in -re add -s, -s, -, -ons, -ez, -ent to the stem.

répondre: je réponds; tu réponds; il, elle, on répond; nous répondons; vous répondez; ils, elles répondent

Some verbs like ouvrir, offrir, and cueillir, although the infinitive ends in -ir, are conjugated like regular -er verbs.

the logical product or the conjunction, denotes the proposition ‘both A and B are true

the logical sum or disjunction, stands for ‘at least one of the propositions, A, B is true’

These symbols are only a shorthand way of writing propositions, and do not stand for numerical values

that A and B have the same truth value, then they are logically equivalent propositions, in the sense that any evidence concerning the truth of one pertains equally well to the truth of the other, and they have the same implications for any further reasoning

The relation between a proposition and its denial is reciprocal

The theory of plausible reasoning based on weak syllogisms is not a ‘weakened’ form of logic; it is an extension of logic with new content not present at all in conventional deductive logic.

a false proposition implies all propositions

merely knowing the truth values of propositions A and B does not provide any information on deducibility

An expression B = f (A 1 ,...,A n ) involving n propositions is a logic function on a space S of M = 2 n points; and there are exactly 2 M such functions.

Since we are, at this stage, restricting our attention to Aristotelian propositions, any logic function C = f (A, B) such as (1.15) has only two possible ‘values’, true and false; and likewise the ‘independent v ariables’ A and B can take on only those two values.

logic functions with only one point being true can be constructed simply by conjunctions of input propositions,

Any logic function that is true on at least one point can be constructed as logical sum of basic conjunctions

the two operations (AND, NOT) already constitute an adequate set for deductive logic

A set of operations suffice to generate all possible logic functions form an adequate set

The duality property shows the logic disjunction \( A + B \) is the same as denying that they are both false \( \overline{ \bar{A} \bar{B} } \)

The operation ‘NAND’ is defined as the negation of ‘AND’

the operation NOR defined by the negation of OR

besides a common ground, a logic gate has two input terminals and one output

We call them ‘desiderata’ rather than ‘axioms’ because they do not assert that anything is ‘true’ but only state what appear to be desirable goals.

We expect plausible reasoning to have no contradictions and be able to determine any unique extension of logic

A ⇒ B is false only if A is true and B is false

The question of logical deducibility of one proposition from a set of others arises in a crucial way in the Gödel theorem

This great difference in the meaning of the word implies in ordinary language and in formal logic is a tricky point that can lead to serious error if it is not properly understood

The theory of plausible reasoning is based on weak syllogisms

Plausible reasoning is an extension of deductive logic because it also applies to weak syllogisms.