Principia Logico-Metaphysica (Draft/Excerpt)
... Consequently, this excerpt omits the Preface, Acknowledgments, Part I (Chapters 1-6), Part II/Chapters 15–16 (which are being reworked), Part III (which is mostly unwritten), and some Appendices in Part IV. The excerpt contains references to some of this omitted content. The work is ongoing and so t ...
... Consequently, this excerpt omits the Preface, Acknowledgments, Part I (Chapters 1-6), Part II/Chapters 15–16 (which are being reworked), Part III (which is mostly unwritten), and some Appendices in Part IV. The excerpt contains references to some of this omitted content. The work is ongoing and so t ...
Independence logic and tuple existence atoms
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
Interpretability formalized
... and for different purposes. A famous and well known example is an interpretation of hyperbolic geometry in Euclidean geometry (e.g., the Beltrami-Klein model, see, for example, [Gre96]) to show the relative consistency of non-Euclidean geometry. Another example, no less famous, is Gödel’s interpret ...
... and for different purposes. A famous and well known example is an interpretation of hyperbolic geometry in Euclidean geometry (e.g., the Beltrami-Klein model, see, for example, [Gre96]) to show the relative consistency of non-Euclidean geometry. Another example, no less famous, is Gödel’s interpret ...
Simply Logical: Intelligent Reasoning by Example
... between clausal logic and Predicate Logic. In Chapter 3, the practical aspects of Prolog programming are discussed. The notion of an SLD-tree forms an important concept in this chapter, most notably in the treatment of cut. When explaining cut, I like to tell my students that it is much like the GO ...
... between clausal logic and Predicate Logic. In Chapter 3, the practical aspects of Prolog programming are discussed. The notion of an SLD-tree forms an important concept in this chapter, most notably in the treatment of cut. When explaining cut, I like to tell my students that it is much like the GO ...
a thesis submitted in partial fulfillment of the requirements for the
... 1.1 Verifying Timing Properties with the Proof Checker Many existing theorem provers are either extremely tedious and/or require skilled users. The thesis presented here is that a simpler proof checker, with a minimal set of inference rules, is powerful enough to verify correctness proofs for real-t ...
... 1.1 Verifying Timing Properties with the Proof Checker Many existing theorem provers are either extremely tedious and/or require skilled users. The thesis presented here is that a simpler proof checker, with a minimal set of inference rules, is powerful enough to verify correctness proofs for real-t ...
Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic
... α . A formula not containing atomic propositions is called a constant formula. To keep the notation simple, we regard the set Φ as fixed, and will usually not mention it explicitly. So we write ML(τ ), or also just ML when τ is clear from the context or irrelevant. We use the same notation for the se ...
... α . A formula not containing atomic propositions is called a constant formula. To keep the notation simple, we regard the set Φ as fixed, and will usually not mention it explicitly. So we write ML(τ ), or also just ML when τ is clear from the context or irrelevant. We use the same notation for the se ...
Graphical Representation of Canonical Proof: Two case studies
... forms of proofs in this formalism are free of bureaucracy, and also canonical from a semantic perspective: for a suitable notion of normal form, they correspond one–to–one with morphisms in free Cartesian closed categories (see e.g. [69]). Another example are Girard’s proof nets for multiplicative l ...
... forms of proofs in this formalism are free of bureaucracy, and also canonical from a semantic perspective: for a suitable notion of normal form, they correspond one–to–one with morphisms in free Cartesian closed categories (see e.g. [69]). Another example are Girard’s proof nets for multiplicative l ...
.pdf
... Thus, changing the environment can affect what properties a program satisfies. Programming logics usually axiomatize program behavior under certain assumptions about the environment. Logics to reason about real-time, for example, axiomatize assumptions about how time advances while the program execu ...
... Thus, changing the environment can affect what properties a program satisfies. Programming logics usually axiomatize program behavior under certain assumptions about the environment. Logics to reason about real-time, for example, axiomatize assumptions about how time advances while the program execu ...
Hilbert`s Program Then and Now
... his view, highlighted in his correspondence with Frege, that consistency of an axiomatic theory guarantees the existence of the structure described, and is in this sense sufficient to justify the use of the theory. And he shared with Kronecker a recognition that elementary arithmetic has a privilege ...
... his view, highlighted in his correspondence with Frege, that consistency of an axiomatic theory guarantees the existence of the structure described, and is in this sense sufficient to justify the use of the theory. And he shared with Kronecker a recognition that elementary arithmetic has a privilege ...
A survey on Interactive Theorem Proving
... provide communication with other users and systems; the essential point, however, is that this new medium is active, whereas paper, for instance, is not. A.Asperti ...
... provide communication with other users and systems; the essential point, however, is that this new medium is active, whereas paper, for instance, is not. A.Asperti ...
Hilbert`s Program Then and Now - Philsci
... term 1920, he concluded that “the aim of reducing set theory, and with it the usual methods of analysis, to logic, has not been achieved today and maybe cannot be achieved at all” [Hilbert, 1920]. At the same time, Brouwer’s intuitionist mathematics gained currency. In particular, Hilbert’s former s ...
... term 1920, he concluded that “the aim of reducing set theory, and with it the usual methods of analysis, to logic, has not been achieved today and maybe cannot be achieved at all” [Hilbert, 1920]. At the same time, Brouwer’s intuitionist mathematics gained currency. In particular, Hilbert’s former s ...
