Semantics: the branch of linguistics concerned with the study of meaning.
The study of meaning is perhaps the least explored of the recognized sub-diciplines of linguistics. The problem stems from the fact that there are very few forms of direct access to the conceptual system of the mind. It is also difficult to differentiate between conceptual structures that are linguistic and those that are not. As a result, there is very little accepted methodology guiding the empirical study of this area. For this reason, many linguists consider semantics, and the conceptual framework in general, to lie outside the realm of linguistics proper.
A good starting point with regard to formal semantic theories is provided by Robin Clark, a linguistics professor at The University of Pennsylvania has a full page of links to course notes dealing with many of these issues. His analysis is thorough and clear but it does assume at least a basic understanding of elementary logic. A similar resource is found in the form of a Web Glossary.
In our Index of Compositional Semantics attempts are made at formalizing compositional interpretation of (sentences within) texts. The goal of this enterprise, of course, is to (formally) describe the relationship between Semantics and Logical Form.
With respect to plural nouns and intervals of time, it soon becomes clear that a certain amount of structure must be imposed on the Domain. A related discipline is the study of the various forms of Quantifiers which delineate and compare various specified subsets of the domain.
One of the central innovations which modern logic has used to complement its classical predecessor is the addition of intensionality to its system. This naiively amounts to the addition of possible worlds. Also central is the introduction of types into the axiom system.
If you've been paying attention, you've probably noticed that this whole semantics thing is somehow related to the notion of 'truth'. Here are some links that attempt to limit their scrutiny to the ever-so-slippery concept of truth.
In recent years, the issue of context has come to the forefront in investigations of linguistic meaning. Context in Linguistic Interpretation provides some interesting links from this domain.
In related work, a new field of dynamic semantics has emerged from the study of context in Natural Language, and an interest in Game-theoretic Logic has re-emerged. In the light of the process/thing confusion that seems to be falling out of modern semantics, another interesting article is this one on Quantum Logic.
For any one with a background in formal logic, an interesting source is the Institute for Logic, Language and Computation Homepage. If you are interested in first-rate formal theory -- particularly in the realm of "dynamic semantics" -- these guys are it. The site includes some published work of some of the institute members, some digging will prove rewarding. Also, check out the The Max Planck Institute for Information. Another good site is the Artificial Intelligence and Computational Logic Group. Another general reference page on the issue of semantics can be found at The Cambridge Theory and Semantics Group. For bibliographical general reference, the Bibliography of Mathematical Logic and Related Fields seems useful --- but some basic German is needed to negotiate the first few pages. For the non-German speakers, there is also a handbook of Artificial Intelligence and Cognitive Science at Birmingham. The International Association of Mathematics and Computer Science has Special issue on Computational Intelligence.
Also closely related here is the concept of Knowledge Structures.
One mistake too frequently made by practicing semanticists is to ignore the social aspect of language use. Happily, this is a mistake that is slowly working its way out of the enterprise.
More from me later. For now, enjoy these links.