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Relational Proposition
Definitions of 2 Basic Key Concepts
1. What is a Proposition? A proposition is
a statement that may either be true or
false
2. A relational proposition is a statement,
which may be true or false and which
shows a relationship between two or
more
entitiespeople,
things,
institutions, animals, etcs.
Relational terms-definitions
• A relational term is a term which
shows the relationship between
two entities (people, places,
things).
• For a relational term to make
sense it must involve more than
one person, object, entity.
• Examples of relational terms-:
friend, lover, teacher, employer,
uncle, student
• There are also phrases that show
the relationship between two
entities- “In front of,” “taller
than,” shorter than
Relational terms act as predicate
• Relational terms are
treated as
predicates. Predicates are expressions
of the form “…is a bird,” …is a house,”
“…are apples,”
• A predicate is the part of a sentence or
clause that contains a verb and which
states something about the subject.
examples
• EXAMPLE 1: Afe Babalola is the university’s
founder. In this example “is the university’s
founder,” is the predicate
• EXAMPLE 2: Afe Babalola is the Chancellor of
Afe Babalola University Ado-Ekiti. In this
example “is the Chancellor” is the predicate
Two types of logical predicate
• A logical predicate may either be MONADIC or
POLYADIC
• A monadic predicate is one which speaks of the
properties of just an individual or just an entity.
• A polyadic predicate deals with the properties of
two or more entities
• EXAMPLE 1 is monadic while EXAMPLE 2 is
polyadic. In Example !, there is only one entity,
which is Afe Babalola. In Example 2, there are two
entities, Afe Babalola and Afe Babalola University.
3 types of Polyadic predicates
• Polyadic predicates express a relation
between two (2) or more relata (sing.relatum)
• 1. Binary/dyadic relation (holds between 2
relata)
• 2. Ternary/triadic relation (holds between 3
relata)
• 3. Tetradic/quarternary relation (holds
between 4 relata)
EXAMPLES (Binary/dyadic relations)
• Binary/dyadic relations (holds between 2
relata).
• Biola is the uncle of Ajala
• Temidayo is a colleague of Noah
• Funmilayo is married to Adekunle
EXAMPLES (Ternary/triadic relation)
• Adekunle, Chioma, and Mohammed are
students.
• Bola is playing with Kunbi and Iyabo
•
EXAMPLE (Tetradic/quarternary
relations )
• ABUAD, EKSU, FedPOAD, College of education
are higher institutions that are not too far
apart.
Direction of relations
• A relation may either be uni-directional or bidirectional
• A uni-directional relation is such that if A shares
the relation to B, B cannot share the relation to A.
The relation goes in one direction only. E.G.
Shade is the wife of Bimbo. In this example “is
the wife” is a relation from Shade to Bimbo and
not in the reverse situation.
• A
B
Direction of relations
• A bi-directional relation is such that if A shares
a relation to B, B shares the same relation to
A.
• A
B
• E.G. Ajani is the spouse of Fumbi. In this
example just as Ajani is the spouse of Fumbi
so is Fumbi the spouse of Ajani
Some attributes of Relations
 Attributes of relations enable us to describe the way
relational terms behave in an argument. 2. to
determine the validity of arguments involving
relational terms
 Relations may have the attribute of being a SYMMETRY,
TRANSITIVITY, or REFLEXIVITY
 The three may further be broken down into three each
 SYMMETRY- symmetrical, asymmetrical, nonsymmetrical
 TRANSITIVITY- Transitive, intransitive, non-transitive
 REFLEXIVITY- reflexive, irreflexive, non-reflexive
SYMMETRY• Binary relations may either be symmetrical,
asymmetrical, or non-symmetrical
• A binary relation is symmetrical when if a
thing has a relation to another, the other thing
has the same relation to the first. I.E. if A has a
relation to B, B has the same relation to A
• E.G. “is the friend of,” “is spouse of”
• A
B
Asymmetrical
• A relation is asymmetrical if when a thing has
a relation to another, the other thing CANNOT
have the relation to it. I.E. if A has a relation to
B, B cannot have the same relation to A.
• E.G. “is taller than,” “is shorter than”
non-symmetrical
• A relation is non-symmetrical when if a thing
has a relation to another, the other thing MAY
or MAY NOT have the same relation to it.
• I.E. if A has a relation to B, B may or may not
have the relation to A
• E.G. “loves,” “is the brother of”
TRANSITIVITY- Transitive, intransitive,
non-transitive
• TRANSITIVITY relation could be transitive,
intransitive, or non-transitive.
• A transitive relation holds between three
relata (A, B,C)
Transitive
• A relation is transitive if when a first thing has
a relation to a second thing and the second
thing has a relation to a third thing, then the
first thing has the same relation to the third
thing. This means that if A has a relation to B
and B has the same relation to C, then A has a
relation to C.
• E.G. “…is taller than…”
Intransitive
• A relation is intransitive if it is such that if
When a first thing has a relation to a second
thing, and the second thing has the same
relation to a third thing then the first thing
cannot have the relation to the third. I.E. if A
has a relation to B and B has a relation to C
then A cannot have that relation to C.
• E.G. “…is the mother of…” “…is five mile away
from”
Nontransitive
• A nontransitive relation is such that if when A
has a relation to B and B has a relation to C
then A may or may not have the same relation
to C. When a first thing has a relation to a
second thing and the second thing has a
relation to a third thing then the first may or
may not have the relation to the third thing
• E.G.: “…is the friend of” “loves”
REFLEXIVITY- reflexive, irreflexive, nonreflexive
Reflexivity has to do with an individual i.e., a
relatum
reflexive
• A reflexive relation holds if an individual can
hold such relation to itself
• “…is identical to…” “…is as tall as…”
• E.G. Kunle is as tall as himself
Irreflexive
• A relation is irreflexive if it is such that a thing
cannot have it to itself
• “is the father of,” “is the sister of” “is married
to”
Non-reflexive
• A relation is non-reflexive if it is such that a
thing may or may not have it to itself
• Love, hate, happy with
Determining the Validity of Arguments
involving Relations
• 1 identify the relational term
• 2 determine the attribute of the relational
term
• 3. consider if the relational term has been
used as it ought to in the argument
• 4. if the relational term has been properly
used then the argument in question is valid
• 5. if the relational term has not been properly
used then the argument in question is invalid