4 research outputs found
Unifiability and Structural Completeness in Relation Algebras and in Products of Modal Logic S5
Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties (in logics) are exhibited. Consequently, RA and products of S5 as well as representable diagonal-free n-dimensional cylindric algebras, RDfn, are almost structurally complete but not structurally complete. In case of S5ⁿ a basis for admissible rules and the form of all passive rules are provided
Supervenience, Dependence, Disjunction
This paper explores variations on and connections between the topics mentioned in its title, using as something of an anchor the discussion in Valentin Goranko and Antti Kuusisto’s “Logics for propositional determinacy and independence”, a venture into what the authors call the logic of determinacy, which they contrast with (a demodalized version of) Jouko Väänänen’s modal dependence logic. As they make clear in their discussion, these logics are closely connected with the topics of noncontingency and supervenience. Two opening sections of the present paper address some of these connections, including related earlier logical work by the present author as well as very recent work by Jie Fan. The Väänänen-inspired treatment is presented in a third section, and then, in Sections 4 and 5, as a kind of centerpiece for the discussion, we follow Goranko and Kuusisto in elaborating one principal reason offered for preferring their own approach over that treatment, which concerns some anomalies over the behaviour of disjunction in the latter treatment. Sections 6 and 7 look at dependence and (several different versions of) disjunction in inquisitive logic, especially as presented by Ivano Ciardelli. Section 8 revisits the less formal property-supervenience literature with issues from the first two sections of the paper in mind, and we conclude with a Postscript addressing a further conceptual issue pertaining to the relation between modal and quantificational dependence logics
Nominal tense logic and other sorted intensional frameworks
This thesis introduces of a system of tense logic called nominal tense logic (NTL), and
several extensions. Its primary aim is to establish that these systems are logically interesting,
and can provide useful models of natural language tense, temporal reference, and
their interaction.
Languages of nominal tense logic are a simple augmentation of Priorean tense logic.
They add to the familiar Priorean languages a new sort of atomic symbol, nominals. Like
propositional variables, nominals are atomic sentences and may be freely combined with
other wffs using the usual connectives. When interpreting these languages we handle the
Priorean components standardly, but insist that nominals must be true at one and only
one time. We can think of nominals as naming this time.
Logically, the change increases the expressive power of tensed languages. There are
certain intuitions about the flow of time, such as irreflexivity, that cannot be expressed
in Priorean languages; with nominals they can. The effects of this increase in expressive
power on the usual model theoretic results for tensed languages discussed, and completeness
and decidability results for several temporally interesting classes of frames are
given. Various extensions of the basic system are also investigated and similar results
are proved. In the final chapter a brief treatment of similarly referential interval based
logics is presented.
As far as natural language semantics is concerned, the change is an important one. A
familiar criticism of Priorean tense logic is that as it lacks any mechanism for temporal
reference, it cannot provide realistic models of natural language temporal usage. Natural
language tense is at least partly about referring to times, and nowadays the deictic and
anaphoric properties of tense are a focus of research. The thesis presents a uniform treatment
of certain temporally referring expressions such as indexicals, and simple discourse
phenomena
Logic and the Foundations of Game and Decision Theory (LOFT 7)
This volume collects together revised papers originally presented at the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2006). LOFT is a key venue for presenting research at the intersection of logic, economics and computer science, and the present collection gives a lively and wide-ranging view of an exciting and rapidly growing area