# Introduction to Situation Theory Part IV

Posted on Fri 22 October 2010 in Situation Theory tutorial

## Situation Semantics

Situation theory was developed to support situation semantics. Natural language semantics are rich and the topic of how to represent these semantics, in situation theory or otherwise, is too complex to give justice to here. We will give a basic account of situation semantics as a situated relational theory of meaning, and work out a few illustrative examples.

### A Theory of Meaning

In situation semantics, the meaning of a sentence is not its propositional content, but a relation between utterance situations involving that sentence and some propositional content.

When a sentence $$\Phi$$, such as I WILL DELIVER HEALTH CARE REFORM, is uttered, it is uttered in some situational context u, the utterance situation. The situation u may be embedded in larger discourse situation d extending u, for example the particular speech in which $$\Phi$$ is uttered. The discourse situation, d, may in turn be regarded as part of a larger embedding situation.which in turn may be embedded in a larger embedding situation, such as the 2008 Presidential election. Interpretation of a sentence may not require that these situations be distinguished. For any particular analysis, it may be the case that u = d = e, or that a more complex hierarchy of contexts is required. We will usually simply refer to the utterance situation u.

In addition to the utterance, discourse, and embedding situation, situation semantics makes use of resource situations. A resource situation r is a situation to which a sentence refers but which is not in the utterance situation. For example the sentence I LOST THE KEYS GIVEN TO ME BY FRANK refers to a situation in the past in which a person named Frank gives the speaker a set of keys. Resource situations are also used to restrict parameters.

The informational content of an assertive sentence is a proposition. Recall that a proposition has as its content s:T, that a situation s is of type T. Generally speaking, it is usually sufficient to regard this as saying that $$s\vDash I$$ where I is the set of infon constituents of T. The propositional content of a sentence like the one above is that there exists a situation in which the speaker has lost a set of keys given to him by Frank. A more formal discussion will follow shortly.

Devlin distinguishes between the abstract meaning of a sentence, a sort of context free meaning of the sentence, and the meaning in use of the sentence. The abstract meaning of a sentence, $$M(\Phi)$$is a relation between the type of the utterance situation and a type of described content. The meaning in use of a sentence, is a relation between a particular utterance situation of a particular type and a particular described content of a particular type, written u|$$\Phi$$|a, where u is the utterance situation, $$\Phi$$ is the sentence, and a the described content.

### A Brief Example: the meaning of YOU

Consider an utterance of the pronoun YOU. What is the meaning of YOU? (Devlin 2006, 15) gives the following analysis:

We define an utterance situation type U, the (parametric) type of situation in which YOU is uttered as:

U(YOU)=[ $$\dot{u} | \dot{u}\vDash <<speakingTo,\dot{a}_{u} ,\dot{b}_{u} ,\dot{l}_{u} ,\dot{t}_{u} ,1>>$$ $$\wedge$$ $$<< utters, \dot{a}_{u}$$ , YOU , $$\dot{l}_{u} , \dot{t}_{u} , 1 >>$$ ]

where $$\dot{u}$$ is a parameter for an utterance situation, $$\dot{a}_{u}$$ is a parameter for a speaker, $$\dot{b}_{u}$$ is a parameter for a listener, and $$\dot{l}_{u}$$ and $$\dot{t}_{u}$$ are parameters for spatial and temporal locations respectively.

The type of described content E may be given by:

$$E=[\dot{b}| \dot{u}<<=,\dot{b},\dot{b}_{u} >>]$$

where $$\dot{b}$$ is an object parameter for the listener, $$\dot{b}_{u}$$ is the parameter found in the utterance type, and = is an equality relation between these two parameters. An object b anchored to $$\dot{b}$$ is of this type if b is the same object as that anchored to the parameter $$\dot{b}_{u}$$ .

The abstract meaning of YOU is the relation between types: U(YOU)[M(YOU)]E.

The meaning in use of a particular utterance of YOU is a relation between the utterance situation supporting that utterance and the descibed content. In particular:

$$u|YOU|b$$ iff $$u:U(YOU)$$ and b=$$b_{u}$$

where we see that and utterance YOU means some person b if the speaker is referring to b.