相关论文: A Universal Approach to Self-Referential Paradoxes…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
We generalize a theorem by Francois Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negation as failure. The study of this relationship is important in connection…
As several different formal systems with inequivalent syntax may describe equivalent semantics, it is possible to find `completions' to more expressive syntaxes that are semantically invariant. Doctrine theory, in the sense of Lawvere, is…
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…
We present a construction of a certain infinite complete partial order (CPO) that differs from the standard construction used in Scott's denotational semantics. In addition, we construct several other infinite CPO's. For some of those, we…
In many expert and everyday reasoning contexts it is very useful to reason on the basis of defeasible assumptions. For instance, if the information at hand is incomplete we often use plausible assumptions, or if the information is…
Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate…
Many writers have observed that default logics appear to contain the "lottery paradox" of probability theory. This arises when a default "proof by contradiction" lets us conclude that a typical X is not a Y where Y is an unusual subclass of…
We show that self-reference can be formalized in Basic logic by means of the new connective @, called "entanglement". In fact, the property of non-idempotence of the connective @ is a metatheorem, which states that a self-entangled sentence…
We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
Simple methods permit to generalize the concepts of iteration and of recursive processes. We shall see briefly on several examples what these methods generate. In additive sequences, we shall encounter not only the golden or the silver…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases,…
To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn…
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…
Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover,…
Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on…