Search results for "modal logic"
showing 10 items of 20 documents
Modal Consequence Relations Extending S4.3: An Application of Projective Unification
2016
We characterize all finitary consequence relations over $\mathbf{S4.3}$ , both syntactically, by exhibiting so-called (admissible) passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic $L$ extending $\mathbf{S4}$ has projective unification if and only if $L$ contains $\mathbf{S4.3}$ . In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, we extend the known results by Bull and Fine, from logics, to consequence relations. We also show that the lattice of consequence relation…
Monadic second-order logic over pictures and recognizability by tiling systems
1994
We show that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system if and only if it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and matches a natural logic. The proof is based on the Ehrenfeucht-FraIsse technique for first-order logic and an implementation of “threshold counting” within tiling systems.
Awareness and partitional information structures
1994
This is the first of two papers where we present a formal model of unawareness. We contrast unawareness with certainty and uncertainty. A subject is certain of something when he knows that thing; he is uncertain when he does not know it, but he knows he does not: he is consciously uncertain. On the other hand, he is unaware of something when he does not know it, and he does not know he does not know, and so on ad infinitum: he does not perceive, does not have in mind, the object of knowledge. The opposite of unawareness is awareness, which includes certainty and uncertainty. This paper has three main purposes. First, we formalize the concept of awareness, and introduce a symmetry axiom whic…
Working with Multiple Ontologies on the Semantic Web.
2016
The standardization of the second generation Web Ontology Language, OWL, leaves a crucial issue for Web-based ontologies unsatisfactorily resolved: how to represent and reason with multiple distinct, but linked, ontologies. OWL provides the owl:imports construct which, roughly, allows Web ontologies to include other Web ontologies, but only by merging all the linked ontologies into a single logical "space". Recent work on multidimensional logics, fusions and other combinations of modal logics, distributed and contextual logics, and the like have tried to find formalisms wherein knowledge bases (and their logic) are kept more distinct but yet affect each other. These formalisms have various …
Frames for fusions of modal logics
2018
Let us consider multimodal logics and . We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and , we construct a connected frame which characterises the fusion . The frame thus obtained has some useful properties. Among others, is countable if both and are countable, and there is a special world of the frame such that any formula is valid in the frame if and only if it is valid at the point . We also describe a similar construction where we assume the existence o…
Phenomenological-Semantic Investigations into Incompleteness
2000
When today the phenomenologist surveys the history of the philosophical comprehension of Godel’s theorems, he is confronted with the realization that the decisive publications come almost exclusively from the sphere of analytic philosophy.1 But does phenomenology in the spirit of Husserl not mean to keep in step with the epochal results of the special sciences by working on the phenomenological understanding of them? Phenomenological research of this kind means the same as development of phenomenological theory of science (Wissenschaftstheorie). In connection with the incompleteness theorems, the latter would be confronted with fundamental questions such as, “To what extent can mathematical…
Awareness and Partitional Informational Structures
1997
We begin with an example to motivate the introduction of the concept of unawareness in models of information. There are a subject and two possible states of the world, σ and τ. At σ a certain fact p happens — it is true — and the subject sees it or hears it or anyhow perceives it, so that he knows it is true (in Geanakoplos [5] the subject is Sherlock Holmes’ assistant and fact p is ‘the dog barks’). At state τ fact p does not occur (it is false), and the subject not only does not see it or hear it etc.; but what is more, he does not even think of the possibility that it might: fact p is not present to the subject’s mind. What is an appropriate formal model for this story?
Elementary Action Systems
2015
This chapter expounds basic notions. An elementary action system is a triple consisting of the set of states, the transition relation between states, and a family of binary relations defined on the set of states. The elements of this family are called atomic actions. Each pair of states belonging to an atomic action is a possible performance of this action. This purely extensional understanding of atomic actions is close to dynamic logic. Compound actions are defined as sets of finite sequences of atomic actions. Thus compound actions are regarded as languages over the alphabet whose elements are atomic actions. This chapter is concerned with the problem of performability of actions and the…
Individuals, Identity, Names: Phenomenological Considerations
1997
In Husserl’s early writings (the Logical Investigations and the first section of Ideas I) the main concern of phenomenological investigations is the givenness of the ideal entities of logic and formal ontology. Another field in his earlier writings is the phenomenology of perception and time consciousness. This field of research broadens into the vision of a universal transcendental aesthetics, which, in his later writings, provides the basis for solving the problem of intersubjectivity.1 The final “synthesis” of these fields and problem domains is to be found in the phenomenological theory of the life-world. Lectures and research manuscripts2 of the late period show also that this second f…
Mathematical logic and quantum finite state automata
2009
AbstractThis paper is a review of the connection between formulas of logic and quantum finite-state automata in respect to the language recognition and acceptance probability of quantum finite-state automata. As is well known, logic has had a great impact on classical computation, it is promising to study the relation between quantum finite-state automata and mathematical logic. After a brief introduction to the connection between classical computation and logic, the required background of the logic and quantum finite-state automata is provided and the results of the connection between quantum finite-state automata and logic are presented.