Abella: A System for Reasoning about Relational Specifications
... The first version of the Abella theorem prover was developed by Andrew Gacek as part of his doctoral work carried out at the University of Minnesota [19]. Kaustuv Chaudhuri and Yuting Wang have subsequently designed and implemented extensions to the system, resulting in an updated release. The vario ...
... The first version of the Abella theorem prover was developed by Andrew Gacek as part of his doctoral work carried out at the University of Minnesota [19]. Kaustuv Chaudhuri and Yuting Wang have subsequently designed and implemented extensions to the system, resulting in an updated release. The vario ...
Goal-directed Proof Theory
... The concept of goal directed computation we adopt can also be seen as a generalization of the notion of uniform proof as introduced in [Miller et al. 91]. As far as we know, a goal-directed presentation have been given of (fragments of) intuitionistic logic [Gabbay and Reyle 84],[Miller 89], [McCart ...
... The concept of goal directed computation we adopt can also be seen as a generalization of the notion of uniform proof as introduced in [Miller et al. 91]. As far as we know, a goal-directed presentation have been given of (fragments of) intuitionistic logic [Gabbay and Reyle 84],[Miller 89], [McCart ...
A survey on Interactive Theorem Proving
... The history of mathematics has stories about false results that went undetected for long periods of time. However, it is generally believed that if a published mathematical argument is not valid, it will be eventually detected as such. While the process of finding a proof may require creative insigh ...
... The history of mathematics has stories about false results that went undetected for long periods of time. However, it is generally believed that if a published mathematical argument is not valid, it will be eventually detected as such. While the process of finding a proof may require creative insigh ...
A Judgmental Reconstruction of Modal Logic
... are true. They are complemented by elimination rules which allow us to obtain further knowledge from the knowledge of compound propositions. The elimination rules for a connective should be locally sound and complete in order to have a satisfactory meaning explanation for the connective. Local sound ...
... are true. They are complemented by elimination rules which allow us to obtain further knowledge from the knowledge of compound propositions. The elimination rules for a connective should be locally sound and complete in order to have a satisfactory meaning explanation for the connective. Local sound ...
Logic and Proof
... Although the patterns of language addressed by Aristotle’s theory of reasoning are limited, we have him to thank for a crucial insight: we can classify valid patterns of inference by their logical form, while abstracting away specific content. It is this fundamental observation that underlies the en ...
... Although the patterns of language addressed by Aristotle’s theory of reasoning are limited, we have him to thank for a crucial insight: we can classify valid patterns of inference by their logical form, while abstracting away specific content. It is this fundamental observation that underlies the en ...
Notes on the Science of Logic
... then reliance on arithmetic or geometrical intuitions would be reasonable; but instead our principal aim is the logical one of seeing how, using only quantifier and truth-functional principles, our conclusions follow from the fundamental axioms and definitions that characterize our subject matter. F ...
... then reliance on arithmetic or geometrical intuitions would be reasonable; but instead our principal aim is the logical one of seeing how, using only quantifier and truth-functional principles, our conclusions follow from the fundamental axioms and definitions that characterize our subject matter. F ...
The History of Categorical Logic
... continuous functions, the category T opGrp of topological groups with continuous homomorphisms and the category Ban of Banach spaces with linear transformations with norm at most 1. This is a surprisingly short list of examples. They give more examples by defining the notion of a subcategory in the ...
... continuous functions, the category T opGrp of topological groups with continuous homomorphisms and the category Ban of Banach spaces with linear transformations with norm at most 1. This is a surprisingly short list of examples. They give more examples by defining the notion of a subcategory in the ...
JUXTAPOSITION - Brown University
... combining logical systems, called “juxtaposition”. I prove general metalogical results concerning the combination of logics by juxtaposition. Second, I examine the particular case of combining classical and intuitionist logics. I show how the general results can be applied to shed light on the pheno ...
... combining logical systems, called “juxtaposition”. I prove general metalogical results concerning the combination of logics by juxtaposition. Second, I examine the particular case of combining classical and intuitionist logics. I show how the general results can be applied to shed light on the pheno ...
On the Complexity of Qualitative Spatial Reasoning: A Maximal
... RCC is a topological approach to qualitative spatial representation and reasoning where spatial regions are subsets of topological space (Randell et al ., 1992) . Relationships between spatial regions are defined in terms of the relation C(a, b) which is true iff the closure of region a is connected ...
... RCC is a topological approach to qualitative spatial representation and reasoning where spatial regions are subsets of topological space (Randell et al ., 1992) . Relationships between spatial regions are defined in terms of the relation C(a, b) which is true iff the closure of region a is connected ...
Discrete Mathematics for Computer Science Some Notes
... our presentation has more of a “computer science” flavor which should make it more easily digestible by our intended audience. Using such a proof system, it is easy to describe very clearly what is a proof by contradiction and to introduce the subtle notion of “constructive proof”. We even question ...
... our presentation has more of a “computer science” flavor which should make it more easily digestible by our intended audience. Using such a proof system, it is easy to describe very clearly what is a proof by contradiction and to introduce the subtle notion of “constructive proof”. We even question ...
A Pebble Weighted Automata and Weighted Logics
... Hoogeboom 1999; Bojańczyk et al. 2006; Samuelides and Segoufin 2007; Bojańczyk 2008], we actually define weighted generalizations that preserve their natural connections with logic. More precisely, we introduce pebble weighted automata on words and establish expressive equivalence to weighted firs ...
... Hoogeboom 1999; Bojańczyk et al. 2006; Samuelides and Segoufin 2007; Bojańczyk 2008], we actually define weighted generalizations that preserve their natural connections with logic. More precisely, we introduce pebble weighted automata on words and establish expressive equivalence to weighted firs ...
Extracting Proofs from Tabled Proof Search
... III History atoms can be tabled; the table only infers its members. IV History atoms can be tabled; the table uses theories to infer additional atoms. The first two strategies yield proof certificates that simply use the cut rule: these two strategies are always sound as long as the theory (in Strat ...
... III History atoms can be tabled; the table only infers its members. IV History atoms can be tabled; the table uses theories to infer additional atoms. The first two strategies yield proof certificates that simply use the cut rule: these two strategies are always sound as long as the theory (in Strat ...
The Foundations
... 3 is a constant, min is a function symbol with arity 2 “min(3,2)” behaves more like x, 3 than “x >y”. So if let P(x,y) “x > y”, then s1 can be represented as P(y, min(x,3)) we call any expression that can be put on the argument position of an atomic proposition a term Obviously, cons ...
... 3 is a constant, min is a function symbol with arity 2 “min(3,2)” behaves more like x, 3 than “x >y”. So if let P(x,y) “x > y”, then s1 can be represented as P(y, min(x,3)) we call any expression that can be put on the argument position of an atomic proposition a term Obviously, cons ...
A causal approach to nonmonotonic reasoning
... since it is based on a direct and transparent description of factual and causal (explanatory) information about the world. In other words, it shows that the epistemic view of nonmonotonic reasoning is not the only possibility. Accordingly, the primary aim of our study will consist in laying down log ...
... since it is based on a direct and transparent description of factual and causal (explanatory) information about the world. In other words, it shows that the epistemic view of nonmonotonic reasoning is not the only possibility. Accordingly, the primary aim of our study will consist in laying down log ...
The Journal of Functional and Logic Programming The MIT Press
... systems where the various domains are built over disjoint signatures and their constraints are processed by different, specialized solvers. In these systems, predicate or function symbols in one signature are applicable, with few exceptions, only to (nonvariable) terms entirely built with symbols fr ...
... systems where the various domains are built over disjoint signatures and their constraints are processed by different, specialized solvers. In these systems, predicate or function symbols in one signature are applicable, with few exceptions, only to (nonvariable) terms entirely built with symbols fr ...
Henkin`s Method and the Completeness Theorem
... individual symbols Henkin means constants and infinitely many variables. It is worth pointing out that Henkin does not have the equality symbol in the alphabet. But we will see that this issue is addressed later in the paper. Task 1: Note that Henkin does not use any function symbols, which became c ...
... individual symbols Henkin means constants and infinitely many variables. It is worth pointing out that Henkin does not have the equality symbol in the alphabet. But we will see that this issue is addressed later in the paper. Task 1: Note that Henkin does not use any function symbols, which became c ...
pdf , 1,18 MB
... none has given rise to more heated debates than the changes in our understanding of science precipitated by the ``quantum revolution''. In this revolution, Niels Bohr's dramatically non-classical theory of the atom proved to be the springboard from which the new atomic physics drew it's momentum. Fu ...
... none has given rise to more heated debates than the changes in our understanding of science precipitated by the ``quantum revolution''. In this revolution, Niels Bohr's dramatically non-classical theory of the atom proved to be the springboard from which the new atomic physics drew it's momentum. Fu ...
Theoretical and observational consistency of Massive Gravity
... Galileon interactions as an important class of infrared modifications of general relativity. We will present their main features and discuss how they can be constructed in the framework of higher dimensional space-time. This will be then an adequate place to illustrate our work of de Sitter Galileon ...
... Galileon interactions as an important class of infrared modifications of general relativity. We will present their main features and discuss how they can be constructed in the framework of higher dimensional space-time. This will be then an adequate place to illustrate our work of de Sitter Galileon ...
HONEST ELEMENTARY DEGREES AND DEGREES OF RELATIVE
... An element a of a lattice cups to an element b > a if there is a c < b such that a ∪ c = b. An element a of a lattice has the cupping property if it cups to every b > a. An element b of a lattice with 0 has the anti-cupping property if there is an a with 0 < a < b that does not cup to b. So, if a, b ...
... An element a of a lattice cups to an element b > a if there is a c < b such that a ∪ c = b. An element a of a lattice has the cupping property if it cups to every b > a. An element b of a lattice with 0 has the anti-cupping property if there is an a with 0 < a < b that does not cup to b. So, if a, b ...
Argumentations and logic
... well-grounded belief is obtainable by humans but that knowledge in the strict sense is beyond our capacity. If no proposition is known to be true, then every argumentation begs the question to everyone and there is no such thing as a proof. Those who believe that knowledge is impossible describe an ...
... well-grounded belief is obtainable by humans but that knowledge in the strict sense is beyond our capacity. If no proposition is known to be true, then every argumentation begs the question to everyone and there is no such thing as a proof. Those who believe that knowledge is impossible describe an ...
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 ...