First-Order Theorem Proving and Vampire
... Which of the following statements are true? 1. First-order logic is an extension of propositional logic; 2. First-order logic is NP-complete. 3. First-order logic is PSPACE-complete. 4. First-order logic is decidable. 5. In first-order logic you can use quantifiers over sets. 6. One can axiomatise i ...
... Which of the following statements are true? 1. First-order logic is an extension of propositional logic; 2. First-order logic is NP-complete. 3. First-order logic is PSPACE-complete. 4. First-order logic is decidable. 5. In first-order logic you can use quantifiers over sets. 6. One can axiomatise i ...
Assumption-Based Argumentation with Preferences
... In this paper we deliver a new formalism, called ABA+ , that extends ABA with preferences, because accounting for preferences is an important aspect of common-sense reasoning (see e.g. [27, 18, 41, 48] for discussions). Indeed, preferences are everyday phenomena helping, for example, to qualify the ...
... In this paper we deliver a new formalism, called ABA+ , that extends ABA with preferences, because accounting for preferences is an important aspect of common-sense reasoning (see e.g. [27, 18, 41, 48] for discussions). Indeed, preferences are everyday phenomena helping, for example, to qualify the ...
PowerPoint
... • Herbrand universe of a program P is now the set of ground terms occurring in it • Herbrand base of P is now the set of ground atoms that can be constructed using predicates in P and terms from the H. universe - representing all the things that could be true or false about relationships between ind ...
... • Herbrand universe of a program P is now the set of ground terms occurring in it • Herbrand base of P is now the set of ground atoms that can be constructed using predicates in P and terms from the H. universe - representing all the things that could be true or false about relationships between ind ...
code-carrying theory - Computer Science at RPI
... proofs actually do prove these theorems, and only if that step succeeds does the consumer apply a “code extractor” to the function-defining axioms to obtain the ...
... proofs actually do prove these theorems, and only if that step succeeds does the consumer apply a “code extractor” to the function-defining axioms to obtain the ...
a thesis submitted in partial fulfillment of the requirements for the
... From a survey of existing theorem provers, it was noted that unpredictable output from inference rules can be frustrating in proof development. The proof checker described here avoids this problem because the user provides the expected result of each step. The use of a functional meta-language as th ...
... From a survey of existing theorem provers, it was noted that unpredictable output from inference rules can be frustrating in proof development. The proof checker described here avoids this problem because the user provides the expected result of each step. The use of a functional meta-language as th ...
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 ...
Saying It with Pictures: a logical landscape of conceptual graphs
... Jaap, Jorge, Nynke, Stephan, Sytske and Valérie, for being a wonderful family. My parents’ encouragement and support mean very much to me. I dedicate this book to Nina and Marieke. My doctoral experience would not have been as exciting without their love and extraordinary patience. ’s Gravenhage Ok ...
... Jaap, Jorge, Nynke, Stephan, Sytske and Valérie, for being a wonderful family. My parents’ encouragement and support mean very much to me. I dedicate this book to Nina and Marieke. My doctoral experience would not have been as exciting without their love and extraordinary patience. ’s Gravenhage Ok ...
Announcement as effort on topological spaces
... must be true for any y ∈ Ui ; but y may not be in Uj , in which case (y, Ui , Uj ) is not well-defined: we cannot interpret K̂j Ki p. Our solution to this dilemma is to consider neighbourhoods that are not only relative to each agent, as usual in multi-agent subset space logics, but that are also re ...
... must be true for any y ∈ Ui ; but y may not be in Uj , in which case (y, Ui , Uj ) is not well-defined: we cannot interpret K̂j Ki p. Our solution to this dilemma is to consider neighbourhoods that are not only relative to each agent, as usual in multi-agent subset space logics, but that are also re ...
Color - Alex Kocurek
... constitute a proof. One can sometimes find rigorous proofs for a variety of inexpressibility claims.8 But only Hodes [1984a,b,c] provides proofs of the inexpressibility of (R), (E), and sentences like them in extensions of first-order modal logic with two-dimensional operators such as @.9 And while ...
... constitute a proof. One can sometimes find rigorous proofs for a variety of inexpressibility claims.8 But only Hodes [1984a,b,c] provides proofs of the inexpressibility of (R), (E), and sentences like them in extensions of first-order modal logic with two-dimensional operators such as @.9 And while ...
PhD Thesis First-Order Logic Investigation of Relativity Theory with
... tacit assumptions. Another reason is that FOL has a complete inference system while second-order logic (and thus any higher-order logic) cannot have one, see, e.g., [20, §IX. ...
... tacit assumptions. Another reason is that FOL has a complete inference system while second-order logic (and thus any higher-order logic) cannot have one, see, e.g., [20, §IX. ...
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 ...
Inductive Types in Constructive Languages
... to inductive definitions (chapter 3), followed by the introduction of the machinery which we require—elementary category theory and algebra (chapter 4). The central part of the treatise consists of the description and justification of inductive types as initial algebras. First, I consider at an abst ...
... to inductive definitions (chapter 3), followed by the introduction of the machinery which we require—elementary category theory and algebra (chapter 4). The central part of the treatise consists of the description and justification of inductive types as initial algebras. First, I consider at an abst ...
Termination of Higher-order Rewrite Systems
... resulting expression may be rewritten again and again, giving rise to a reduction sequence. Such a sequence can be seen as a computation. Certain expressions are considered as results, or normal forms. A computation terminates successfully when such a normal form has been reached. This situation can ...
... resulting expression may be rewritten again and again, giving rise to a reduction sequence. Such a sequence can be seen as a computation. Certain expressions are considered as results, or normal forms. A computation terminates successfully when such a normal form has been reached. This situation can ...
TR-14-06 - Ynot - Harvard University
... Importantly, Q can depend not only upon the return value x, but also the initial and final stores making it possible to capture relational properties of stateful computations in the style of Standard Relational Semantics well-known in the research on Hoare Logic for first-order languages [12]. In o ...
... Importantly, Q can depend not only upon the return value x, but also the initial and final stores making it possible to capture relational properties of stateful computations in the style of Standard Relational Semantics well-known in the research on Hoare Logic for first-order languages [12]. In o ...
Simplicity, Truth, and Topology Kevin T. Kelly Konstantin Genin Hanti Lin
... (Akaike, 1974; Forster and Sober, 1994; Vapnik, 1998), but that instrumentalistic approach falls short of justifying belief in the theories, themselves. At the opposite extreme, Bayesians can post arbitrarily high betting quotients on inductive conclusions, and can explain Ockham’s razor in a ratio ...
... (Akaike, 1974; Forster and Sober, 1994; Vapnik, 1998), but that instrumentalistic approach falls short of justifying belief in the theories, themselves. At the opposite extreme, Bayesians can post arbitrarily high betting quotients on inductive conclusions, and can explain Ockham’s razor in a ratio ...
How to Write a 21st Century Proof
... The prose proof’s third sentence, “But f 0 (x ) > 0 . . . ” asserts two facts, so let’s turn them into steps 3 and 4 of the structured proof. The final sentence could also be viewed as two statements, but I find it more natural to turn it into the assertion f (b) > f (a) and its proof. Adding these ...
... The prose proof’s third sentence, “But f 0 (x ) > 0 . . . ” asserts two facts, so let’s turn them into steps 3 and 4 of the structured proof. The final sentence could also be viewed as two statements, but I find it more natural to turn it into the assertion f (b) > f (a) and its proof. Adding these ...
The Z/EVES 2.0 User`s Guide - Department of Computer Science
... this declaration before use order. Documents often present Z specifications with the paragraphs out of order; if such a specification is imported into Z/EVES it is necessary to move the paragraphs into a suitable checking order. Order is also important for theorems, as the proof of a given theorem c ...
... this declaration before use order. Documents often present Z specifications with the paragraphs out of order; if such a specification is imported into Z/EVES it is necessary to move the paragraphs into a suitable checking order. Order is also important for theorems, as the proof of a given theorem c ...
Foundations of Databases - Free University of Bozen
... descendent of(X, Y) ← child of(X, Y). descendent of(X, Y) ← descendent of(X, Z), descendent of(Z, Y). ← descendent of(karl, X). ...
... descendent of(X, Y) ← child of(X, Y). descendent of(X, Y) ← descendent of(X, Z), descendent of(Z, Y). ← descendent of(karl, X). ...