a-logic - Digital [email protected] State University

... Whitehead’s great book, Principia Mathematica (1913) of Quine’s Mathematical Logic (1940) and Methods of Logic (4th ed.,1982) and of hundreds of other textbooks and treatises which have the same set of theorems, the same semantical foundations, and use the same concepts of validity and logical truth ...

... Whitehead’s great book, Principia Mathematica (1913) of Quine’s Mathematical Logic (1940) and Methods of Logic (4th ed.,1982) and of hundreds of other textbooks and treatises which have the same set of theorems, the same semantical foundations, and use the same concepts of validity and logical truth ...

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 ...

Principles of Model Checking

... The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics ...

... The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics ...

The Liar Paradox: A Consistent and Semantically Closed Solution

... This thesis develops a new approach to the formal denition of a truth predicate that allows a consistent, semantically closed denition within classical logic. The approach is built on an analysis of structural properties of languages that make Liar Sentences and the paradoxical argument possible. ...

... This thesis develops a new approach to the formal denition of a truth predicate that allows a consistent, semantically closed denition within classical logic. The approach is built on an analysis of structural properties of languages that make Liar Sentences and the paradoxical argument possible. ...

On Weak Ground

... condition is stated in terms of sequents with an arbitrary set of sentences φ0 , φ1 , ... on the left-hand side. ...

... condition is stated in terms of sequents with an arbitrary set of sentences φ0 , φ1 , ... on the left-hand side. ...

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 ...

Chapter 9

... separately or together and for ind’s considered alone. Proof Unrestricted implication implies finite implication by definition. For fd’s and jd’s taken separately or together, Theorem 8.4.12 on the relationship between chasing and logical implication can be used to obtain the opposite implication. F ...

... separately or together and for ind’s considered alone. Proof Unrestricted implication implies finite implication by definition. For fd’s and jd’s taken separately or together, Theorem 8.4.12 on the relationship between chasing and logical implication can be used to obtain the opposite implication. F ...

PhD Thesis First-Order Logic Investigation of Relativity Theory with

... [2, §3.4], [3]. More boldly: it is superfluous as an axiom because it is provable as a theorem from much simpler and more convincing basic assumptions. The linearity of ...

... [2, §3.4], [3]. More boldly: it is superfluous as an axiom because it is provable as a theorem from much simpler and more convincing basic assumptions. The linearity of ...

Incompleteness

... For every formula φpxq the axiom rφp0q ^ @x pφpxq Ñ φpx ` 1qqs Ñ @x φpxq We let PA denote the Peano axioms scheme, and let F denote PA minus the induction axioms. Thus, F is a finite set of axioms. Note that F just says that the various functions and relations are correctly computed at Spyq from the ...

... For every formula φpxq the axiom rφp0q ^ @x pφpxq Ñ φpx ` 1qqs Ñ @x φpxq We let PA denote the Peano axioms scheme, and let F denote PA minus the induction axioms. Thus, F is a finite set of axioms. Note that F just says that the various functions and relations are correctly computed at Spyq from the ...

Introduction to Computational Logic

... and interactive theorem proving with the proof assistant Coq. At Saarland University the course is taught in this format since 2010. Students are expected to be familiar with basic functional programming and the structure of mathematical definitions and proofs. Talented students at Saarland Universi ...

... and interactive theorem proving with the proof assistant Coq. At Saarland University the course is taught in this format since 2010. Students are expected to be familiar with basic functional programming and the structure of mathematical definitions and proofs. Talented students at Saarland Universi ...

Graphical Representation of Canonical Proof: Two case studies

... and cut elimination corresponds to computation. If cut reduction is confluent, then the computation it embodies is deterministic, which in many cases means the proof system may be employed, more or less directly, as a language of computation. One of Girard’s original motivations for proof nets was t ...

... and cut elimination corresponds to computation. If cut reduction is confluent, then the computation it embodies is deterministic, which in many cases means the proof system may be employed, more or less directly, as a language of computation. One of Girard’s original motivations for proof nets was t ...

A counterexample-guided abstraction

... as Markov Decision Processes (MDP). Abstractions have been extensively studied in the context of probabilistic systems with definitions for good abstractions and specific families of abstractions being identified (see Section 6). In this paper, like Jonsson and Larsen [1991], D’Argenio et al. [2001] ...

... as Markov Decision Processes (MDP). Abstractions have been extensively studied in the context of probabilistic systems with definitions for good abstractions and specific families of abstractions being identified (see Section 6). In this paper, like Jonsson and Larsen [1991], D’Argenio et al. [2001] ...

Principia Logico-Metaphysica (Draft/Excerpt)

... In this and subsequent chapters, our metalanguage makes use of informal notions and principles about numbers and sets so as to more precisely articulate and render certain definitions. These are not primitive notions or principles of our metaphysical system; ultimately, they are to be understood by ...

... In this and subsequent chapters, our metalanguage makes use of informal notions and principles about numbers and sets so as to more precisely articulate and render certain definitions. These are not primitive notions or principles of our metaphysical system; ultimately, they are to be understood by ...

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 ...