The Journal of Functional and Logic Programming The MIT Press
... what concerns mathematical logic in general, and [JM94] for what concerns constraint logic programming in particular. We report here the most notable notational conventions followed. Further notation, which may appear in the sequel, follows the common conventions of the two fields. The letters v, x, ...
... what concerns mathematical logic in general, and [JM94] for what concerns constraint logic programming in particular. We report here the most notable notational conventions followed. Further notation, which may appear in the sequel, follows the common conventions of the two fields. The letters v, x, ...
A Unified View of Induction Reasoning for First-Order Logic
... and implicit induction principles, [16, 22, 27, 30, 40, 56] being among the most notable. Other studies have been conducted to reduce the gap between them. Protzen [42] proposed a proof strategy to perform lazy induction on particular explicit induction proofs. Kapur and Subramaniam [29] devised a m ...
... and implicit induction principles, [16, 22, 27, 30, 40, 56] being among the most notable. Other studies have been conducted to reduce the gap between them. Protzen [42] proposed a proof strategy to perform lazy induction on particular explicit induction proofs. Kapur and Subramaniam [29] devised a m ...
logic for the mathematical
... Then there are four chapters on 1st order logic, each analogous to the one four earlier on propositional logic. One feature of the proof theory is that we deal with both common approaches to the treatment of non-sentence formulae, giving the appropriate deduction theorem and completeness (and a slig ...
... Then there are four chapters on 1st order logic, each analogous to the one four earlier on propositional logic. One feature of the proof theory is that we deal with both common approaches to the treatment of non-sentence formulae, giving the appropriate deduction theorem and completeness (and a slig ...
CS 208: Automata Theory and Logic
... – Introduced by Alan Turing as a simple model capable of expressing any imaginable computation – Turing machines are widely accepted as a synonyms for algorithmic computability (Church-Turing thesis) – Using these conceptual machines Turing showed that first-order logic validity problem a is non-com ...
... – Introduced by Alan Turing as a simple model capable of expressing any imaginable computation – Turing machines are widely accepted as a synonyms for algorithmic computability (Church-Turing thesis) – Using these conceptual machines Turing showed that first-order logic validity problem a is non-com ...
Predicate Logic
... False. 3 is a counterexample. the set of positive integers not exceeding 4: {1, 2, 3, 4} False. 3 is a counterexample. Also note that here ∀P (x) is P (1) ∧ P (2) ∧ P (3) ∧ P (4), so its enough to observe that P (3) is false. the set of real numbers in the interval [10, 39.5] True. It takes a bit lo ...
... False. 3 is a counterexample. the set of positive integers not exceeding 4: {1, 2, 3, 4} False. 3 is a counterexample. Also note that here ∀P (x) is P (1) ∧ P (2) ∧ P (3) ∧ P (4), so its enough to observe that P (3) is false. the set of real numbers in the interval [10, 39.5] True. It takes a bit lo ...
Understanding SPKI/SDSI Using First-Order Logic
... An identifier is a word over some given standard alphabet. The set of all identifiers is denoted by A, and an identifier is denoted by A or B (often with subscripts). We assume that both K and A are countable. We do not consider SDSI 1.1 [30] special roots, which are identifiers that are bound to th ...
... An identifier is a word over some given standard alphabet. The set of all identifiers is denoted by A, and an identifier is denoted by A or B (often with subscripts). We assume that both K and A are countable. We do not consider SDSI 1.1 [30] special roots, which are identifiers that are bound to th ...
thèse - IRIT
... the truth value of a propositional variable here or there, if possible. These atomic programs are then combined by the usual dynamic logic connectives. The resulting formalism is called dynamic here-and-there logic (D-HT), and it allows for atomic change of equilibrium models. Moreover, we relate D- ...
... the truth value of a propositional variable here or there, if possible. These atomic programs are then combined by the usual dynamic logic connectives. The resulting formalism is called dynamic here-and-there logic (D-HT), and it allows for atomic change of equilibrium models. Moreover, we relate D- ...
Reasoning about Complex Actions with Incomplete Knowledge: A
... proposals [10,24,9,26,18] and it allows very natural representation of actions as state transitions, through the accessibility relation of Kripke structures. We introduce an action theory on the line of [6,18,19], in which actions are represented by modalities, and we extend it by allowing sensing a ...
... proposals [10,24,9,26,18] and it allows very natural representation of actions as state transitions, through the accessibility relation of Kripke structures. We introduce an action theory on the line of [6,18,19], in which actions are represented by modalities, and we extend it by allowing sensing a ...
Combinaison des logiques temporelle et déontique pour la
... stay very pleasant. I learnt a lot about deontic logics and action logics. The collaboration that followed was really stimulating until the end of my PhD, and the logic proposed in this dissertation is its fruit. My acknowledgment then goes to Philippe Balbiani, for all the discussions we had, about ...
... stay very pleasant. I learnt a lot about deontic logics and action logics. The collaboration that followed was really stimulating until the end of my PhD, and the logic proposed in this dissertation is its fruit. My acknowledgment then goes to Philippe Balbiani, for all the discussions we had, about ...
First-Order Theorem Proving and VAMPIRE
... simplifying ones. This distinction will be made more clear when we later discuss saturation and redundancy elimination in Section 4. Though the most complex part of proof search is the use of the resolution and superposition inference system, preprocessing is also very important, especially when the ...
... simplifying ones. This distinction will be made more clear when we later discuss saturation and redundancy elimination in Section 4. Though the most complex part of proof search is the use of the resolution and superposition inference system, preprocessing is also very important, especially when the ...
How to Write a 21st Century Proof
... This has two consequences: proofs are unnecessarily hard to understand, and they encourage sloppiness that leads to errors. Making proofs easier to understand is easy. It requires only the simple application of two principles: structure and naming. When one reads a sentence in a prose proof, it is o ...
... This has two consequences: proofs are unnecessarily hard to understand, and they encourage sloppiness that leads to errors. Making proofs easier to understand is easy. It requires only the simple application of two principles: structure and naming. When one reads a sentence in a prose proof, it is o ...
Dialectica Interpretations A Categorical Analysis
... The Girard category together with a Girardian comonad yields a model of linear logic with modality, so we get a collection of realizability models for linear logic with modality. The construction from a fibration p : E → T to its Dialectica category Dial(p) contains an implicit soundness proof. Info ...
... The Girard category together with a Girardian comonad yields a model of linear logic with modality, so we get a collection of realizability models for linear logic with modality. The construction from a fibration p : E → T to its Dialectica category Dial(p) contains an implicit soundness proof. Info ...
logic, programming and prolog (2ed)
... are discussed. Finally some alternative approaches based on three-valued logics are described to explain alternative views of negation in logic programming. The final chapter of Part I introduces two notions available in existing Prolog systems. Cut is introduced as a mechanism for reducing the over ...
... are discussed. Finally some alternative approaches based on three-valued logics are described to explain alternative views of negation in logic programming. The final chapter of Part I introduces two notions available in existing Prolog systems. Cut is introduced as a mechanism for reducing the over ...
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 ...
Discrete Mathematics
... In this course, we’ll be writing theorems and their proofs in the Isabelle/Isar proof language. ...
... In this course, we’ll be writing theorems and their proofs in the Isabelle/Isar proof language. ...
