An Overview of Intuitionistic and Linear Logic
... Constructivism is a point of view concerning the concepts and methods used in mathematical proofs, with preference towards constructive concepts and methods. It emerged in the late 19th century, as a response to the increasing use of abstracts concepts and methods in proofs in mathematics. Kronecker ...
... Constructivism is a point of view concerning the concepts and methods used in mathematical proofs, with preference towards constructive concepts and methods. It emerged in the late 19th century, as a response to the increasing use of abstracts concepts and methods in proofs in mathematics. Kronecker ...
An Introduction to Prolog Programming
... A short introduction can be found in the notes; for more details refer to theoretically oriented books on logic programming. ...
... A short introduction can be found in the notes; for more details refer to theoretically oriented books on logic programming. ...
full text (.pdf)
... We formulate a noncommutative sequent calculus for partial correctness that subsumes propositional Hoare Logic. Partial correctness assertions are represented by intuitionistic linear implication. We prove soundness and completeness over relational and trace models. As a corollary we obtain a comple ...
... We formulate a noncommutative sequent calculus for partial correctness that subsumes propositional Hoare Logic. Partial correctness assertions are represented by intuitionistic linear implication. We prove soundness and completeness over relational and trace models. As a corollary we obtain a comple ...
SORT LOGIC AND FOUNDATIONS OF MATHEMATICS 1
... Institute for Logic, Language and Computation University of Amsterdam, The Netherlands [email protected] I have argued elsewhere [8] that second order logic provides a foundation for mathematics much in the same way as set theory does, despite the fact that the former is second order and th ...
... Institute for Logic, Language and Computation University of Amsterdam, The Netherlands [email protected] I have argued elsewhere [8] that second order logic provides a foundation for mathematics much in the same way as set theory does, despite the fact that the former is second order and th ...
Nonmonotonic Reasoning - Computer Science Department
... reasoning is true in all intended interpretations (or models) in which the premises are true. A ”completeness and correctness theorem” for a system says that the ”safe” rules of deduction in the textbooks generate exactly all those conclusions from premises which are true in every interpretation in ...
... reasoning is true in all intended interpretations (or models) in which the premises are true. A ”completeness and correctness theorem” for a system says that the ”safe” rules of deduction in the textbooks generate exactly all those conclusions from premises which are true in every interpretation in ...
A Well-Founded Semantics for Logic Programs with Abstract
... model semantics was first proposed for normal logic programs by Gelfond and Lifschitz in 1988, various extensions have been put forward for theoretical and/or practical reasons. These include disjunctive logic programs (Gelfond and Lifschitz 1991), nested logic programs (Lifschitz, Tang, and Turner ...
... model semantics was first proposed for normal logic programs by Gelfond and Lifschitz in 1988, various extensions have been put forward for theoretical and/or practical reasons. These include disjunctive logic programs (Gelfond and Lifschitz 1991), nested logic programs (Lifschitz, Tang, and Turner ...
LOGIC MAY BE SIMPLE Logic, Congruence - Jean
... We must thus distinguish the fact that a structure – is an algebra, – can be conceived as an algebra. A distributive complemented lattice is strictly speaking a cross-structure involving an algebraic structure and a structure of order, but it can be conceived as a pure algebraic structure, in partic ...
... We must thus distinguish the fact that a structure – is an algebra, – can be conceived as an algebra. A distributive complemented lattice is strictly speaking a cross-structure involving an algebraic structure and a structure of order, but it can be conceived as a pure algebraic structure, in partic ...
Discrete Mathematics - Lecture 4: Propositional Logic and Predicate
... less than 20 faculty and at least one noble laureate. B. All universities in USA where every department has at least 20 faculty and at least one noble laureate. C. For all universities in USA there is a department has less than 20 faculty or at most one noble laureate. D. For all universities in USA ...
... less than 20 faculty and at least one noble laureate. B. All universities in USA where every department has at least 20 faculty and at least one noble laureate. C. For all universities in USA there is a department has less than 20 faculty or at most one noble laureate. D. For all universities in USA ...
Normal modal logics (Syntactic characterisations)
... Systems of modal logic In common with most modern approaches, we will define systems of modal logic (‘modal logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ ...
... Systems of modal logic In common with most modern approaches, we will define systems of modal logic (‘modal logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ ...
Tactics for Separation Logic Abstract Andrew W. Appel INRIA Rocquencourt & Princeton University
... proving an imperative program, much of the reasoning is not about memory cells but concerns the abstract mathematical objects that the program’s data structures represent. Lemmas about those objects are most conveniently proved in a general-purpose higher-order logic, especially when there are large ...
... proving an imperative program, much of the reasoning is not about memory cells but concerns the abstract mathematical objects that the program’s data structures represent. Lemmas about those objects are most conveniently proved in a general-purpose higher-order logic, especially when there are large ...
INTERPLAYS OF KNOWLEDGE AND NON
... complete with respect to some given class of Kripke frames, in the same way normal modal logics are (see [14]). Since the work developed in [7], a lot of important results have appeared in the domain of epistemic logics. Many authors have studied these systems especially concerning applications in C ...
... complete with respect to some given class of Kripke frames, in the same way normal modal logics are (see [14]). Since the work developed in [7], a lot of important results have appeared in the domain of epistemic logics. Many authors have studied these systems especially concerning applications in C ...
Admissible rules in the implication-- negation fragment of intuitionistic logic
... Although a logic may not be structurally complete, there may be well-behaved sets of formulas such that for rules whose premises form such a set, admissibility coincides with derivability. Let us fix L as a logic based on a language L containing a binary connective → for which modus ponens is deriva ...
... Although a logic may not be structurally complete, there may be well-behaved sets of formulas such that for rules whose premises form such a set, admissibility coincides with derivability. Let us fix L as a logic based on a language L containing a binary connective → for which modus ponens is deriva ...
INTRODUCTION TO LOGIC Natural Deduction
... One way of showing that an argument is valid is to break it down into several steps and to show that one can arrive at the conclusion through some more obvious arguments. It’s not clear one can break down every valid argument into a sequence of steps from a predefined finite set of rules. This is po ...
... One way of showing that an argument is valid is to break it down into several steps and to show that one can arrive at the conclusion through some more obvious arguments. It’s not clear one can break down every valid argument into a sequence of steps from a predefined finite set of rules. This is po ...
Propositional inquisitive logic: a survey
... Inquisitive semantics stems from a line of work which, going back to [12], has aimed at providing a uniform semantic foundation for the interpretation of both statements and questions. The approach was developed in an early version, based on pairs of models, in [13], [16]; it reached the present for ...
... Inquisitive semantics stems from a line of work which, going back to [12], has aimed at providing a uniform semantic foundation for the interpretation of both statements and questions. The approach was developed in an early version, based on pairs of models, in [13], [16]; it reached the present for ...
Systems of modal logic - Department of Computing
... Systems of modal logic In common with most modern approaches, we will define systems of modal logic (‘modal logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ ...
... Systems of modal logic In common with most modern approaches, we will define systems of modal logic (‘modal logics’ or just ‘logics’ for short) in rather abstract terms — a system of modal logic is just a set of formulas satisfying certain closure conditions. A formula A is a theorem of the system Σ ...
Logical nihilism - University of Notre Dame
... is incomplete with respect to this semantics, and more plausibly one should say that this reading of `IPC φ ⊃ ψ is erroneous. Thus we see a sense in which the phenomenon of structural completeness is related to a sort of semantic completeness: A structurally incomplete logic will be incomplete with ...
... is incomplete with respect to this semantics, and more plausibly one should say that this reading of `IPC φ ⊃ ψ is erroneous. Thus we see a sense in which the phenomenon of structural completeness is related to a sort of semantic completeness: A structurally incomplete logic will be incomplete with ...
Proof theory of witnessed G¨odel logic: a
... As usual a formula is valid if it is evaluated to 1 under every interpretation. Remark 1 Taking different subsets V of [0, 1] closed under infima and suprema and containing both 0 and 1 as truth values give rise to different sets of valid formulas, that is they lead to different Gödel logics. As sh ...
... As usual a formula is valid if it is evaluated to 1 under every interpretation. Remark 1 Taking different subsets V of [0, 1] closed under infima and suprema and containing both 0 and 1 as truth values give rise to different sets of valid formulas, that is they lead to different Gödel logics. As sh ...
Quantified Equilibrium Logic and the First Order Logic of Here
... Tech. Report MA-06-02 (Univ. of Málaga, Spain) ...
... Tech. Report MA-06-02 (Univ. of Málaga, Spain) ...
sentential logic
... Formal systems of logic are also interesting in their own right. Logicians and mathematicians are interested in finding out what they can or cannot prove, and also their many other logical properties. Formal systems of logic also play an important role in understanding the foundations of set theory ...
... Formal systems of logic are also interesting in their own right. Logicians and mathematicians are interested in finding out what they can or cannot prove, and also their many other logical properties. Formal systems of logic also play an important role in understanding the foundations of set theory ...
page 3 A CONVERSE BARCAN FORMULA IN ARISTOTLE`S
... T2 [b](a)’ shows that one individual human {this human} runs or another individual human {that human} different from the first is running. ⊥ is a proposition-forming quantifier/qualifier limiting the reference range of the bracketed subject and general term b to a specific individual as it shows tha ...
... T2 [b](a)’ shows that one individual human {this human} runs or another individual human {that human} different from the first is running. ⊥ is a proposition-forming quantifier/qualifier limiting the reference range of the bracketed subject and general term b to a specific individual as it shows tha ...
propositions and connectives propositions and connectives
... propositions names: p, q, r, …, p0, p1, p2, … a name for false : ...
... propositions names: p, q, r, …, p0, p1, p2, … a name for false : ...
Document
... two-valued logic – every sentence is either true or false some sentences are minimal – no proper part which is also a sentence others – can be taken apart into smaller parts we can build larger sentences from smaller ones by using connectives ...
... two-valued logic – every sentence is either true or false some sentences are minimal – no proper part which is also a sentence others – can be taken apart into smaller parts we can build larger sentences from smaller ones by using connectives ...
Propositional Logic
... • Algorithmically simple but more complex than perfect induction. • Not considered appropriate for general problem solving. ...
... • Algorithmically simple but more complex than perfect induction. • Not considered appropriate for general problem solving. ...
GLukG logic and its application for non-monotonic reasoning
... to a designated value. The most simple example of a multivalued logic is classical logic where: D = {0, 1}, 1 is the unique designated value, and connectives are defined through the usual basic truth tables. If X is any logic, we write |=X α to denote that α is a tautology in the logic X. We say V t ...
... to a designated value. The most simple example of a multivalued logic is classical logic where: D = {0, 1}, 1 is the unique designated value, and connectives are defined through the usual basic truth tables. If X is any logic, we write |=X α to denote that α is a tautology in the logic X. We say V t ...
A Proof of Nominalism. An Exercise in Successful
... Another mixed case seems to be obtainable by considering the higher-order logic known as type theory as a many-sorted first-order theory, each different type serving as one of the “sorts”. One can try to interpret the logics of Frege and of Russell and Whitehead in this way. The attempt fails (syste ...
... Another mixed case seems to be obtainable by considering the higher-order logic known as type theory as a many-sorted first-order theory, each different type serving as one of the “sorts”. One can try to interpret the logics of Frege and of Russell and Whitehead in this way. The attempt fails (syste ...