Search results for "Modal logic"
showing 10 items of 20 documents
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…
Monadic Second-Order Logic over Rectangular Pictures and Recognizability by Tiling Systems
1996
Abstract It is shown that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system iff 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 also 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.
Plantinga’s Haecceitism and Simple Quantified Modal Logic
2017
In a series of papers Alvin Plantinga argued for a serious actualist modal semantics based on the notions of possible world, understood as maximal possible state of affairs, and of individual essence (haecceity). Plantinga’s actualism is known as haecceitism. In spite of the fact that haecceitism has been thought by Plantinga to require a Kripke-style semantics, the aim of this paper is to show that it is compatible with constant domains semantics and the simplest quantified modal logic. I will argue that not only does this approach have all the advantages of a greater simplicity in combining quantification and modalities, but also it better conforms to the actualist program.
A calculus for robot inner speech and self-awareness
2019
The inner speech is the common mental experience the humans have when they dialogue with themselves. It is widely acknowledged that inner speech is related to awareness and self-awareness. The inner speech reproduces and expands in the mind social and physical sources of awareness. In this preliminary work, a calculus based on a first-order modal logic to automate inner speech is presented. It attempts to make the existing inner speech theories suitable for robot. By making robot able to talk to itself, it is possible to analyze the role of inner speech in robot awareness and self-awareness, opening new interesting research scenarios not yet investigated.
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…
Projective unification in transitive modal logics
2018
We show that a transitive normal modal logic L enjoys projective unification (i.e. each unifiable formula is projective) if and only if L contains K4D1 ( D1 : ( x → y ) ∨ ( y → x ) ). It means, in particular, that K4D1 (and any of its extensions) is almost structurally complete, i.e. the logic is complete with respect to all non-passive admissible rules. We also characterize non-unifiable formulas and provide an explicit form of the basis for all passive rules over K4G + ( x → x )
Employing fuzzy logic in the diagnosis of a clinical case
2010
Fuzzy logic is a logical calculus which operates with many truth values (while classical logic works with the two values of true and false). Since fuzzy logic considers the truth of scientific statements like something softened, it is fruitfully applied to the study of biological phenomena, biology is indeed considered the field of complexity, uncertainty and vagueness. In this paper fuzzy logic is successfully applied to the clinical diagnosis of a patient who suffers from different diseases bound by a complex causal chain. In this work it is presented a mathematical foundation of fuzzy logic (with connectives and inference rules) and then the application of fuzzy reasoning to the study of…
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 …
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…
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…