Situation Semantics

Origin. Jon Barwise and John Perry, Situations and Attitudes (MIT Press, 1983), following Barwise's "Scenes and other situations" (1981). The driving argument was linguistic: naked-infinitive perception reports — "Ralph saw Mary run" — permit substitution of coreferring terms and support existential generalization, yet fail to be closed under logical equivalence, which no possible-worlds semantics can deliver. Keith Devlin, Logic and Information (1991), gave the infon algebra; Barwise and Etchemendy, The Liar (1987), applied the framework to semantic paradox using Aczel's anti-foundation axiom; Barwise and Seligman, Information Flow (1997), developed the constraint machinery into channel theory.

Models. Situations are partial: parts of the world, not total ways the world might be, and a situation may support an infon, support its dual, or neither. A possible world is the limiting case, a maximal consistent situation. Information is carried by constraints — lawful relations between situation types — so meaning is a relation between an utterance situation and a described situation rather than a set of worlds.

Formalism.

Situations: s: actual partial state of affairs. Not total (unlike possible worlds). Part of reality. Located, concrete.

Infons: ⟨⟨R, a₁,...,aₙ; 1⟩⟩: R holds of a₁,...,aₙ. ⟨⟨R, a₁,...,aₙ; 0⟩⟩: R doesn't hold. Basic information units. Polarity included.

Support: s ⊨ σ: situation s supports infon σ. s makes σ true. May be partial: neither supports nor denies. Partiality key.

Situation types: Type S: situations satisfying conditions. s : S means s is of type S. Abstract situations. Classification.

Constraints: S₁ ⇒ S₂: situations of type S₁ are of type S₂. Lawful connections. Carry information. Ecological.

Information carried: If s : S₁ and S₁ ⇒ S₂, then s carries info that S₂. Smoke carries info of fire. Constraint-based meaning. Ecological semantics.

Persistence: If s ⊨ σ and s ⊑ s', then s' ⊨ σ. Information survives enlargement; ignorance does not. Negative facts require the dual infon, not failure to support.

Propositions: Austinian: a proposition is a pair {s ; σ} — a situation together with a type. True iff s ⊨ σ. The described situation is part of the proposition, not of the context. Two utterances of one sentence express different propositions if they describe different situations.

Meaning as a relation: u ⟦φ⟧ s: utterance situation u describes situation s. One sentence, many utterances, many described situations. Barwise and Perry's "efficiency of language."

The Liar (Barwise–Etchemendy 1987): Circular propositions are modelled in Aczel's non-well-founded set theory (AFA). The Liar is a genuine Austinian proposition, false at its own situation. The paradoxical reasoning is diagnosed as an equivocation on which situation is described.

Symbols.

Symbol	Unicode	Name	Meaning
s	—	Situation	A partial state of affairs
σ	U+03C3	Sigma / Infon	A discrete item of information
⊨	U+22A8	Supports	s ⊨ σ: the situation makes the infon hold
⟨⟨R,a;i⟩⟩	—	Infon	Relation, arguments, and polarity i ∈ {0,1}
⇒	U+21D2	Constraint	Lawful relation between situation types
⊑	U+2291	Part of	s ⊑ s': persistence runs upward along this
:	—	Typing	s : S — situation s is of type S
{s ; σ}	—	Austinian proposition	Situation paired with a type
⟦φ⟧	—	Meaning relation	Relation between utterance and described situation
AFA	—	Anti-foundation axiom	Aczel's set theory, used for circular propositions

Metatheory. Partiality is the central feature, and it is what makes the attitude semantics non-classical: since infons are not closed under logical consequence, an agent related to one situation type is not thereby related to its consequences, so the framework avoids logical omniscience by construction rather than by stipulation. Structurally the theory imposes persistence — if s ⊨ σ and s ⊑ s' then s' ⊨ σ — so the part-of order carries information upward but not ignorance; falsity requires the dual infon and is not mere failure to support, which is where bivalence is given up. Possible-worlds semantics is recovered as the maximal case, so situation semantics is a proper refinement rather than a rival. Barwise and Etchemendy (1987) modelled circular propositions in Aczel's anti-foundation axiom and diagnosed the Liar as a false Austinian proposition whose paradoxical derivation equivocates on the described situation. Kratzer's situation semantics (from 1989) is the descendant that survived in linguistics, treating situations as parts of worlds.

Applies to. Semantics. Information theory. Context. Situated cognition.

Limitations. There is no canonical formalization: Barwise and Perry's, Devlin's infon algebra, and Barwise and Etchemendy's set-theoretic version differ in the axioms on situations, and no completeness or decidability result attaches to "situation semantics" as such — the theory offers a model class without a proof system. Constraints are primitive and unreduced, so the account of information flow presupposes exactly the lawful connections it is meant to explain. Modelling circular propositions requires abandoning foundation for AFA, a substantive set-theoretic commitment. The ontology is heavy — partial facts, polarities, situation types, and a part-of order on reality — and none of it is independently motivated by the semantics. Compositionality is weaker than in the Montagovian tradition, since meaning is a relation between situations rather than a function computed from constituents, and it is the Kratzer-style reconstruction, not this one, that current linguistic semantics uses.