Expansion of logical connections: Difference between revisions

From Lojban
Jump to navigation Jump to search
m (→‎Interactions with scope: Adding one further expansion for clarity)
m (→‎Interactions with scope: Adding a couple of missing -s)
Line 51: Line 51:


When a bridi connective is followed by the "nai" suffix, this means that the right-hand side of the connection is negated; when it is preceded by the "na" connective prefix, this means the left-hand side of the connection is negated.
When a bridi connective is followed by the "nai" suffix, this means that the right-hand side of the connection is negated; when it is preceded by the "na" connective prefix, this means the left-hand side of the connection is negated.
In both case, the negation scope over that of any scope-generating word or construct located within the target side of the connection.
In both cases, the negation scopes over that of any scope-generating word or construct located within the target side of the connection.
However, in the case of bridi-tail connections, the whole bridi-tail connection is under the scope of any scope-generating word located in the shared bridi-head.
However, in the case of bridi-tail connections, the whole bridi-tail connection is under the scope of any scope-generating word located in the shared bridi-head.



Revision as of 11:22, 1 August 2014

Full bridi connections

Forethought:   { GA mi brode gi do brodo }
Afterthought:  { mi brode .i JA do brodo }

Full bridi connectives encodes a relation between two statements (du'u abstractions), and can be expressed using the appropriate predicate word:

  • kaxyje'u = both statements x1 (du'u) and x2 (du'u) are true (logical conjunction)
  • vlinyje'u = at least one of the statements x1 (du'u) and x2 (du'u) is true (logical disjunction)
  • (...)

Therefore, the bridi connection { ga mi brode gi do brodo } can be rephrased as below:

  • vlinyje'u fa lo du'u mi brode kei lo du'u do brodo

Bridi-tail connections

Forethought:   { mi GA [ brode ti ] gi [ brodo tu ] vau do }
Afterthought:  { mi [ brode ti ] GIhA [ brodo tu ] vau do }

=  GA mi brode ti do gi mi brodo tu do
=  mi brode ti do .i JA mi brodo tu do


Sumti connections

Forethought:   { GA mi gi do broda }
Afterthought:  { mi A do broda }

=  GA mi broda gi do broda
=  mi broda .i JA do broda


Multiple sumti connections

mi .a do ti .o tu broda

=  ga [ go mi ti broda gi mi tu broda ] gi [ go do ti broda gi do tu broda ]


Interactions with scope

When a bridi connective is followed by the "nai" suffix, this means that the right-hand side of the connection is negated; when it is preceded by the "na" connective prefix, this means the left-hand side of the connection is negated. In both cases, the negation scopes over that of any scope-generating word or construct located within the target side of the connection. However, in the case of bridi-tail connections, the whole bridi-tail connection is under the scope of any scope-generating word located in the shared bridi-head.

Examples:

• brode .i na ja nai brodo
= naku brode .i ja naku brodo

• ro da brode de na gi'a nai brodo di
= ro da brode naku de gi'a brodo naku di
= ro da brode naku de .i ja ro da brodo naku di

In the case of sumti connectives, a negative connective affix (na, nai) will scope over the connected sumti, as shown in the example below:

• da broda ro brodo na .e de di
= da broda ro brodo na gi'e broda de vau di
= da broda naku ro brodo di .i je da broda de di