Related papers: Logic and Paradox
Program logics for bug-finding (such as the recently introduced Incorrectness Logic) have framed correctness and incorrectness as dual concepts requiring different logical foundations. In this paper, we argue that a single unified theory…
Two types of approximation to the paradoxical Russell Set are presented, one approximating it from below, one from above. It is shown that any lower approximation gives rise to a better approximation containing it, and that any upper…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
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…
Much of philosophical logic and all of philosophy of language make empirical claims about the vernacular natural language. They presume semantics under which `and' and `or' are related by the dually paired distributive and absorption laws.…
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…
In this paper we analyse some of the classical paradoxes in Social Choice Theory (namely, the Condorcet paradox, the discursive dilemma, the Ostrogorski paradox and the multiple election paradox) using a general framework for the study of…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…
The fundamental aim of the paper is to correct an harmful way to interpret a Goedel's erroneous remark at the Congress of Koenigsberg in 1930. Despite the Goedel's fault is rather venial, its misreading has produced and continues to produce…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…
A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…
This short squib looks at how using a broader definition of G\"odel numbering to mimic the accessibility relation between possible worlds results in two-world systems that sidestep undecidable sentences as well as the Liar paradox.
Modern Logics, as formulated notably by Frege, Russell and Tarski involved basic assumptions about Natural Languages in general and Indo-European Languages in particular, which are contested by Linguists. Based upon those assumptions,…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest…
In this paper, we discuss different models for human logic systems and describe a game with nature. Godel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry breaking.…
This is an examination, a commentary, of links between some philosophical views ascribed to G\"odel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from…
The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical…