Usase of connectives is a part of propositional calculus 
which allows assertions like: the book is on the table, or 
“if Socrates is a man, then he is mortal”. 
Actually, the meaning of connections is used in order to 
defend their natural interpretation, so that, if X and Y are 
two statements: 
X a Y is true when both X and Y are true: otherwise it is 
false 
X v Y is true if X is true or Y is true or both 
X -, is true when X is false, and is false when X is true 
X -> Y the truth of X implies that Y is true 
X = Y is true if both X and Y are true, or both X and Y 
are false. 
From syntactic combination of variables and connectives, 
one can build sentences of propositional logic, just like 
the expressions of mathematics. In the propositional 
calculus, one also encounters the first rules of inference. 
An inference rule allows for the deduction of a new 
sentence from previously given sentences: the new 
sentence is assured to be true, if the previous sentences 
(X a (X -> F)) F 
were true. An example of inference rule is the 
“-»’’elimination rule: 
the buildings denote the human settlements 
the schools belong to the class of buildings 
the schools are located inside the human settlements. 
For the purposes of AI, propositional logic is not very 
useful. In order to capture in a formalism the world , one 
needs not only express true or false sentences, but also to 
speak about objects: the predicate calculus is an extension 
of the propositional calculus. 
Statements about individuals are called predicates', a 
predicate has a value of either true or false, where 
individuals are used: the school is a building or the 
railways is a building. 
Use of quantifiers V and 3 implies the introduction of 
four inference rules; if: 
0(A) 
V can be eliminated: 
VX.&(X) 
all rivers have an end-point; 
the Po is a river; 
the Po has an end-point. 
Functions return objects related to their arguments: the 
function capital of, when applied to the individual Italy 
returns the value Rome. The predicate calculus, with 
addition of functions, and the predicate equals is called 
First Order Logic. 
Various Artificial Intelligence systems use logic to 
represent knowledge, but it is to keep in mind that, 
besides logical formalism, also other formalisms are 
available: 
■ procedural representation 
■ semantic networks 
■ production systems 
■ direct representations. 
Discrimination between declarative and procedural 
representations of knowledge played an important role in 
development of AI. Declarative representations state the 
static pattern of knowledge (facts involving subjects, 
events and their intercourse) Procedural representations 
refer to usage of knowledge (how to find basic facts, or 
draw conclusions). All computation programs include 
some type of procedural knowledge. 
4. Modern Linguistics 
Modem Linguistic is commonly said to originate as late 
as the V century b.c., although in the proper sense, its 
birth may be place much close to the present , that is 
about 1916 (de Saussure), or even 1926 (Trubeckoj): 
according to the philosophical viewpoint, also Chomsky 
(1956) may be taken as one of the founders of this 
discipline. Actually, Linguistics is a complex of 
comparatively antique notions, however organized only 
in quite recent times. 
The interest for Sanskrit which peaked for some decades, 
after Von Humboldt (1786-1816), gave a remarkable 
impulse to what one nowerdays is called Lingusitics, as it 
originated comparative grammar, taking into account 
some methods derived in the same period for natural 
sciences. 
However de Saussure upset the historical viewpoint of 
studies about language, clearly declaring that the basis of 
Linguistics relies upon the study of real working of 
language. The primary item is unity: de Saussure, in fact, 
tried to individuate the real units which make up the so 
called chaine-parlee, the units of code that make the 
messages is called structural analysis. 
A further step in this analysis is the subdivision of 
chaine-parlee, in elementary, individual units, from the 
phonic point of view. This way, the basic concept of 
phoneme comes to light as found by Trubeckoj (1890- 
1938). The reconaissance, as identical units, of all the 
single i spoken by all possible voices. So, phonemes are 
signs, which work opposite to each other, in order to 
discriminate different meanings. 
Natural language has a double articulation of speech. 
Units of first articulation of language, the ones which 
compose the message, may be brought to light: such units 
are called monemes and their individuation is easier than 
definition of speech. 
Messages of natural languages also hold a further 
articulation: monemes are, in their turn, decomposed in 
smaller units which can be detected by commutation. 
Those minimal units which have a phonic form, but no 
ordinary meaning are the minimal elements of the second 
articulation: they are properly the phonemes, as found by 
Trubeckoj (incidentally, he too of Pregel club, like 
Jakobson). 
The said structure of a double, superimposed code has 
been hitherto found only in the natural human languages. 
Mathematics, also mathematical logics, are 
communication systems for which minimal units of the 
message are meaningful, with a form and a semantic