...Retrieval
This work has been carried out in the framework of project FERMI 8134 - ``Formalization and Experimentation in the Retrieval of Multimedia Information'', funded by the European Community under the ESPRIT Basic Research scheme. This paper will appear in the Proceedings of SIGIR-94, 17th ACM International Conference on Research and Development in Information Retrieval, Dublin, 1994.
...Sebastiani
Current address: Department of Computing Science, University of Glasgow, G12 8QQ Glasgow, United Kingdom. E-mail: fabrizio@dcs.glasgow.ac.uk
...logic
TLs may in fact be regarded as fragments of first-order logic.
...TLs
For reasons of space we will not give the formal semantics of the term-forming operators of MIRTL here; the interested reader is referred either to [8] or to the full paper [9]. The informal meaning of these operators is the following:

We will also use the following shorthands:
...show
In the full paper [9] we also consider formulae of type where either or may be an individual constant. This allows the expression of probability terms such as (appears-in), which expresses the ``probability that a randomly picked appears in the SIGIR93 proceedings''.
...structures
In most approaches based on PWS, interpretations are called ``possible worlds''; we avoid using this terminology here, both because it has often given rise to misunderstandings about the meaning of ``possible'', and because we want to highlight the relationship of containment between the semantics of MIRTL and the semantics of -MIRTL. It is worthwhile to notice that, in the same way that possible worlds for e.g. sentential modal logic are truth value assignments (to the formulae of sentential logic) that comply with the intuitive meaning of the connectives of sentential logic, interpretations are assignments of ``extensions'' (to concepts, roles and individual constants) that comply with the intuitive meaning of the operators of MIRTL. It is thus clear that ``classical'' (sentential) possible worlds stand to sentential logic as our interpretations stand to MIRTL.
...them
Readers familiar with PWS for modal logic might have noticed that, unlike what normally happens for formulae whose interpretation depends on a multiplicity of ``possible worlds'', there is no ``accessibility relation'' involved in the computation of degrees of belief. This is not inconsistent with the principles underlying PWS, as it is well-known (see e.g. [pages 334-335]Halpern92) that using the set of all worlds belonging to a modal structure is equivalent to using only the set of worlds that are ``accessible'' through an equivalence relation. -MIRTL is then conceptually similar to the S5 modal logic; analogously to what happens in S5, terms representing degrees of belief have the same extension in all interpretations belonging to the same PTL structure.

Fabrizio_Sebastiani