The Saptbhangi syllogism comes from the vacch nay tradition (Syadvad) of tools, rules, modules and methods for reasoning and discourse. Its paradigm is that words are the means for the mind to mind communication. Words in a conversation express cognized awareness of sense inputs about an object of concern (pramey) to create the awareness of the object that listener can cognize. A shared cognition mediated by words is normative of argumentation and such words also facilitate further reasoning about the object. Equivocation in assertions and doubt (syad) in propositions about an object beyond direct scrutiny are minimized with independent evidence (praman) to affirm assertions, to verify and calibrate propositions. Doubtful propositions tentatively retain information in unresolved or undecided affirmed assertions that may otherwise be discarded. This syllogism provides a framework for wide ranging logics to resolve semantic arguments as well as self-reference paradoxes .

The Saptbhangi inference propositions develop in two steps from assertion about an object of concern. First, equivocation in an assertion is minimized with independent evidence, or it may be rephrased to conform to the evidence. Eight propositions are obtained from three assertions that equivocate existence of an object. The first assertion "asti" for it exists (A) may be affirmed on the basis of observable and measurable sense inputs from the object. Its cognized awareness forms the basis of its word description. The second assertion "avaktavya" for it is undescribable (U) is for example affirmed if the awareness of the object is not described. A tangible object also exhibits context dependent action and behavior consequences. The third assertion "nasti" for it does not exist (N) is for example affirmed if the object has no context-dependent action and behavior consequences of its presence versus its absence. NAU assertions in a proposition together relate to the cognized sense inputs for word description and for reasoning of the consequences of an object. The set of eight NAU propositions in Table 1 is a template for the possible relations to be interpreted for an inference: 

Propositions with N (does not exist), A (exists), and U (undescribable) assertions affirmed (+) or not-affirmed (-) by evidence

1 - - - 0 0 0
2 - + - 0 1 0
3 - - + 0 0 1
4 - + + 0 1 1
5 + - - 1 0 0
6 + + - 1 1 0
7 + - + 1 0 1
8 + + + 1 1 1

1. May be it is emptiness of nothing or null with no affirmed assertion. [N-A-U-] node (0 0 0) of maximum equivocation accommodates the affirmed assertions for the other seven propositions. 
2. May be it exists is a true (T) proposition for affirmed existence (A+) supported by not affirmed non-existence and is not asserted as undescribable: (0 1 0) or [N-A+U-].
3. May be it is undescribable is a false (F) proposition for not affirmed existence or non-existence asserted as undescribable: (0 0 1) or [N-A-U+].
4. May be it exists asserted as undescribable is a doubtful (D) proposition for not affirmed nonexistence and affirmed existence yet undescribable: (0 1 1) or [N-A+U+]. 
5. May be it does not exist is a valid proposition for affirmed non-existence that is consistent with not affirmed existence and is not undescribable: (1 0 0) or [N+A-U-]. 
6. May be it is a contradiction of affirmed existence and affirmed non-existence that is not affirmed as undescribable: (1 1 0) or [N+A+U-]. 
7. May be it does not exist with affirmed nonexistence and not affirmed existence and undescribable: (1 0 1) or [N+A-U+]. 
8. May be it is a contradiction of affirmed existence and affirmed non-existence and also undescribable: (1 1 1) or [N+A+U+]. 

The logical inference of each of the propositions tentatively follows from its affirmed assertions. As in sculpting a rock, the criteria-based identity of the object emerges as a particular and as a member of a class by carving away the extraneous to minimize equivocation with evidence and to resolve inconsistencies and eliminate contradictions with additional assertions. N-A-U- (0 0 0) is the maximally noncommittal null (X) proposition with no affirmed input for the three assertions. Validity of each of the other seven propositions is calibrated with its affirmed assertions. N-A+U- (0 1 0) rephrased as A+N-D- is it exists, and not non-exists, and not un-describable. Congruence of A+ with orthogonal and inversely complementary N- and U- provides a consistent cognitive basis to interpret it as a true proposition (T) that paves the way to identify, conceptualize and verify and represent the existence. The total number of propositions (2n) increases exponentially with the number of assertions (n). The X and T position remain the same but with additional support. However, the others with contradictory, inconsistent or invalid assertions may be interpreted as false (F) or doubtful (D). If the identified contradictory states are discarded, the focus of reasoning would be to minimize the D in relation to the identified T and F states. 

A distinguishing feature of the saptbhangi syllogism with equivocating orthogonal assertion is that it considers validity of evidence to affirm an assertion separately from the validity of the logical inference from the relations between the assertions in a proposition. For example in the binary proposition A+N- affirmed existence is supported by independent not affirmed non-existence. Three relations are apparent if the proposition read as combined assertion of "existence AND NOT non-existence". Assertion A+ is logically related to N- with the connectives AND & NOT. Thus as a valid proposition A+N- asserted A+ and also the implied N-. It makes it a logically consistent with the proposition A+ NAND N+. In the binary logic NAND is abbreviation for NOT-AND that corresponds to not both. Other binary connectives are derived from NAND. In effect, two different kinds of negations implicit in NAND are distinguished as non- and NOT for the validation by evidence from the validation by logical connectives in a sapthbhangi proposition.

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