Context-Sensitive Operations
Chapter Forty
Syllabus topic Module 1, "Context-sensitive operations"
Pages 131 to 133 of 378
In one line
A rule that says "do this here" has to say what counts as here, and Pāṇini says it with a case ending.
In the wording you can write in an examination: a context-sensitive operation is one whose applicability depends on the material surrounding the element operated on, not only on that element. In the Aṣṭādhyāyī the context is stated by the case ending of the word naming it: by sūtra 1.1.66 a locative means the operation applies to what precedes the named item, and by sūtra 1.1.67 an ablative means it applies to what follows. In formal language theory a context-sensitive rule is one whose left-hand side is longer than a single symbol.
Why a rule needs a context at all
Consider an operation: a vowel is lengthened. When?
"Always" is wrong, because the language is full of short vowels. "Before an ending" is a context. "After a particular root" is a different context. "Between two consonants" is a third.
So nearly every interesting rule is a triple: what is changed, what it becomes, and where. The first two are the operation and the third is the context, and a grammar needs a notation for all three.
Pāṇini's notation: the case endings do the work
This is one of the most economical devices in the whole grammar, and it is stated as two meta-rules.
Sūtra 1.1.66, tasminniti nirdiṣṭe pūrvasya. When something is named in the locative case, the operation applies to what stands BEFORE it.
Sūtra 1.1.67, tasmād ity uttarasya. When something is named in the ablative case, the operation applies to what stands AFTER it.
Both numbers are confirmed in the digital sūtrapāṭha.
So the grammatical case of a word in a rule tells you where the operation happens. No separate notation for context is needed at all: the language's own morphology carries it.
The three ways a rule names its environment
| Case used | What it means | Where the operation lands |
|---|---|---|
| genitive | "of X" | X itself is what is replaced. This is the operand, not the context |
| locative | "in the presence of X", by 1.1.66 | on what precedes X |
| ablative | "after X", by 1.1.67 | on what follows X |
Read those three together and the whole triple is expressible. The genitive names the thing changed, the locative and the ablative name the neighbourhood, and a rule that uses all three has stated an operation in context in a few words.
And the genitive is itself governed by a meta-rule. Sūtra 1.1.49, ṣaṣṭhī sthāneyogā, confirmed in the sūtrapāṭha, provides that a genitive in a rule is to be understood as "in the place of". So "of X" means "in the place of X", which is a substitution.
Context-Sensitive Operations
Worked example: reading a rule's context
Take 7.3.84, whose translation Vasu gives as: when a sārvadhātuka or an ārdhadhātuka affix follows there is guṇa of the base.
The affix is named in the locative. So by 1.1.66 the operation applies to what precedes the affix, which is the base. That is where the words "of the base" in Vasu's English come from: they are the effect of the case ending plus the meta-rule.
Guṇa is the operation, and what it replaces is supplied by 1.1.3, as [Meta-Rules: Paribhāṣā, and Rules About Rules] shows.
So the rule's four parts are: operand, the base's ik vowel; result, its guṇa; context, a following affix of two named kinds; and the context's direction, given by a case ending read through a meta-rule.
Nothing in the rule says the word "before" or "after". The case ending says it. That is the economy.
The formal meaning of context-sensitive
The phrase has a precise meaning in formal language theory and it is not the same as the informal one. It is worth having both.
A context-free rule has exactly one symbol on its left-hand side. It says: wherever you see this one symbol, you may replace it, no matter what surrounds it.
A -> b C d
A context-sensitive rule has more than one symbol on its left-hand side, so the surroundings are part of what must match.
x A y -> x b y
Here A becomes b, but only between x and y, and the x and y are unchanged. The rule cannot be split into a context-free one without losing the condition.
The consequence, which is the important part. Context-sensitive grammars generate strictly more languages than context-free ones. So the question "is the Aṣṭādhyāyī context-free?" is a real question with real stakes, and [Context-Free Grammar, and Whether Pāṇini Wrote One] answers it.
Where the Aṣṭādhyāyī is context-free and where it is not
Some rules are context-free in the formal sense. A rule that introduces an affix because the meaning requires it names no environment; it just adds material.
Most operational rules are not. 7.3.84 requires a following affix of a particular kind, which is context. Written as a rewrite rule its left-hand side has to mention both the vowel and the affix, so it has more than one symbol.
And some rules are worse than context-sensitive in the formal sense. A rule whose condition refers to a marker that has already been deleted, or to whether another rule has fired, is not a rewrite rule over strings at all. The asiddhatva mechanism of [Asiddhatva and the Tripādī: Ordering by Blocking] is exactly that, and it is why the formal classification of the whole grammar is not a simple matter.
Context-Sensitive Operations
The honest summary. The Aṣṭādhyāyī is a rule system with contexts, and the formal hierarchy is a tool for comparing it with modern grammars rather than a box it fits into. An answer that says so is better than one that picks a class.
What context-sensitivity is NOT
It is not the same as having exceptions. An exception is another rule. A context is a condition inside one rule.
It is not the same as ambiguity. A context makes a rule narrower, and narrower rules make a grammar more determinate, not less.
It is not expensive by itself. Checking a context costs a look at the neighbours. What is expensive is deciding which of several context-sensitive rules applies, which is why the precedence principles exist.
Quick revision
- Nearly every rule is a triple: what is changed, what it becomes, and where.
- Pāṇini states the "where" with a case ending. 1.1.66: a locative means the operation applies to what precedes. 1.1.67: an ablative means it applies to what follows.
- 1.1.49 ṣaṣṭhī sthāneyogā: a genitive means "in the place of", so "of X" is a substitution for X.
- Formally, a context-free rule has one symbol on its left; a context-sensitive rule has more, so the surroundings must match and are preserved.
- Context-sensitive grammars generate strictly more languages than context-free ones.
- The Aṣṭādhyāyī has context-free rules, many context-sensitive ones, and mechanisms that are not string rewriting at all.
Test yourself
1. How does a rule of the Aṣṭādhyāyī say where an operation applies?
By the case ending of the word naming the neighbouring item. By 1.1.66 a locative means the operation applies to what precedes it; by 1.1.67 an ablative means it applies to what follows.
2. What does a genitive in a rule mean, and which sūtra says so?
It means "in the place of", so the item named in the genitive is what is replaced. Sūtra 1.1.49, ṣaṣṭhī sthāneyogā.
3. Give the formal definition of a context-sensitive rule and one example.
A rule whose left-hand side has more than one symbol, so that the surrounding material must match and is preserved. For example x A y rewrites to x b y, which replaces A by b only between x and y.
4. Why is "is the Aṣṭādhyāyī context-free?" a question with stakes?
Because context-sensitive grammars generate strictly more languages than context-free ones, so the answer says something about what kind of system the grammar is, and about whether a context-free formalism could express it.
The rest of this subject
These notes are cut from the University's printed syllabus. Open the syllabus itself for the same subject.