Proof Methods for Corecursive Programs
... As an example, if types are modelled as sets, then a type of infinite lists of integers can be defined as the greatest set X for which there is a bijection X ∼ = Z × X, and hence any function that produces such an infinite list is (according to our definition) a corecursive program. Similarly, a typ ...
... As an example, if types are modelled as sets, then a type of infinite lists of integers can be defined as the greatest set X for which there is a bijection X ∼ = Z × X, and hence any function that produces such an infinite list is (according to our definition) a corecursive program. Similarly, a typ ...
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... However, in many seemingly analogous cases we do have termination nevertheless, e.g. for the rewrite system for the Hydra battle [Mos09, Fle07], since the terms one obtains are simpler in some specifiable sense. It turns out that in the present situation the crux is, as becomes clear from Kripke’s f ...
... However, in many seemingly analogous cases we do have termination nevertheless, e.g. for the rewrite system for the Hydra battle [Mos09, Fle07], since the terms one obtains are simpler in some specifiable sense. It turns out that in the present situation the crux is, as becomes clear from Kripke’s f ...
ppt - Rensselaer Polytechnic Institute: Computer Science
... properties, independent of the existence of other (possibly malicious) entities (either computations or humans) in the system • What properties must a language have to be secure? • One way to make a language secure is to base it on capabilities – A capability is an unforgeable language entity (« tic ...
... properties, independent of the existence of other (possibly malicious) entities (either computations or humans) in the system • What properties must a language have to be secure? • One way to make a language secure is to base it on capabilities – A capability is an unforgeable language entity (« tic ...
IOSR Journal of VLSI and Signal Processing (IOSR-JVSP)
... conditional transition from 01. The introduction of static inverter has the additional advantage that fanout of gate is driven by static inverter with low impedance output which increases noise immunity. Also it reduces the capacitance of dynamic output node. Since each dynamic gate has static inve ...
... conditional transition from 01. The introduction of static inverter has the additional advantage that fanout of gate is driven by static inverter with low impedance output which increases noise immunity. Also it reduces the capacitance of dynamic output node. Since each dynamic gate has static inve ...
Specifying and Verifying Fault-Tolerant Systems
... on TLA, the Temporal Logic of Actions. The semantics of TLA is defined in terms of states and behaviors. A state is an assignment of values to variables, and a behavior is an infinite sequence of states. A TLA formula is interpreted as a boolean function on behaviors. In TLA, a system is modeled by ch ...
... on TLA, the Temporal Logic of Actions. The semantics of TLA is defined in terms of states and behaviors. A state is an assignment of values to variables, and a behavior is an infinite sequence of states. A TLA formula is interpreted as a boolean function on behaviors. In TLA, a system is modeled by ch ...
Language, Proof and Logic
... the logically equivalent sentence ∀x [x = x → S(x)]. Or, if our language has the predicate Thing(x) that holds of everything in the domain of discourse, we could use general conditional proof to obtain ∀x [Thing(x) → S(x)]. But since general conditional proof may not allow us to prove ∀x S(x) alone, ...
... the logically equivalent sentence ∀x [x = x → S(x)]. Or, if our language has the predicate Thing(x) that holds of everything in the domain of discourse, we could use general conditional proof to obtain ∀x [Thing(x) → S(x)]. But since general conditional proof may not allow us to prove ∀x S(x) alone, ...
Reductio ad Absurdum Argumentation in Normal Logic
... define, in several ways, the meaning, the semantics of a Logic Program. Several semantics were defined, some 2-valued, some 3-valued, and even multi-valued semantics. The current standard 2-valued semantics for Normal Logic Programs— the Stable Models Semantics [11] — has been around for almost 20 y ...
... define, in several ways, the meaning, the semantics of a Logic Program. Several semantics were defined, some 2-valued, some 3-valued, and even multi-valued semantics. The current standard 2-valued semantics for Normal Logic Programs— the Stable Models Semantics [11] — has been around for almost 20 y ...
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 ...
Incompleteness in the finite domain
... tures without any formal supporting evidence. There are, essentially, two reasons for stating some sentences as conjectures. First, we believe that some basic theorems of proof theory should also hold true with suitable bounds on the lengths of proofs. The prime example is the Second Incompleteness ...
... tures without any formal supporting evidence. There are, essentially, two reasons for stating some sentences as conjectures. First, we believe that some basic theorems of proof theory should also hold true with suitable bounds on the lengths of proofs. The prime example is the Second Incompleteness ...
MATH20302 Propositional Logic
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
Incompleteness in the finite domain
... tures without any formal supporting evidence. There are, essentially, two reasons for stating some sentences as conjectures. First, we believe that some basic theorems of proof theory should also hold true with suitable bounds on the lengths of proofs. The prime example is the Second Incompleteness ...
... tures without any formal supporting evidence. There are, essentially, two reasons for stating some sentences as conjectures. First, we believe that some basic theorems of proof theory should also hold true with suitable bounds on the lengths of proofs. The prime example is the Second Incompleteness ...
Let me begin by reminding you of a number of passages ranging
... maximally general science. As Frege says in the opening paragraph of “Der Gedanke”, The word ‘law’ is used in two senses. When we speak of moral or civil laws we mean prescriptions which ought to be obeyed but with which actual occurrences are not always in conformity. Laws of nature [on the other h ...
... maximally general science. As Frege says in the opening paragraph of “Der Gedanke”, The word ‘law’ is used in two senses. When we speak of moral or civil laws we mean prescriptions which ought to be obeyed but with which actual occurrences are not always in conformity. Laws of nature [on the other h ...
The Project Gutenberg EBook of The Algebra of Logic, by Louis
... erroneous idea, arising from a simple confusion of thought, that algebraical symbols necessarily imply something quantitative, for the antagonism there used to be and is on the part of those logicians who were not and are not mathematicians, to symbolic logic. This idea of a universal mathematics w ...
... erroneous idea, arising from a simple confusion of thought, that algebraical symbols necessarily imply something quantitative, for the antagonism there used to be and is on the part of those logicians who were not and are not mathematicians, to symbolic logic. This idea of a universal mathematics w ...
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.