Sequent Combinators: A Hilbert System for the Lambda
... • By introducing basic principles of reasoning and then proving in the metatheory that the deduction theorem holds, saying that if B is provable under hypothesis A then A ⇒ B is provable. We shall call such systems Hilbert systems. • By including the deduction theorem as a rule of inference, making ...
... • By introducing basic principles of reasoning and then proving in the metatheory that the deduction theorem holds, saying that if B is provable under hypothesis A then A ⇒ B is provable. We shall call such systems Hilbert systems. • By including the deduction theorem as a rule of inference, making ...
SLD-Resolution And Logic Programming (PROLOG)
... one still needs to define the semantics of logic programs in some independent fashion. This will be done in Subsection 9.5.4, using a model-theoretic semantics. Then, the correctness of SLD-resolution (as a computation procedure) with respect to the model-theoretic semantics will be proved. In this ...
... one still needs to define the semantics of logic programs in some independent fashion. This will be done in Subsection 9.5.4, using a model-theoretic semantics. Then, the correctness of SLD-resolution (as a computation procedure) with respect to the model-theoretic semantics will be proved. In this ...
Provability as a Modal Operator with the models of PA as the Worlds
... If we consider the pointed submodels of M (which include some node A and all of its decendants) which such submodels are isomorphic to each other (in the sense of graph structure alone), how many isomorphism classes are there? We know that if B is sound and satisfies the Hilbert Bernays conditions, ...
... If we consider the pointed submodels of M (which include some node A and all of its decendants) which such submodels are isomorphic to each other (in the sense of graph structure alone), how many isomorphism classes are there? We know that if B is sound and satisfies the Hilbert Bernays conditions, ...
abdullah_thesis_slides.pdf
... Given d,t ∈ N, we can define the concept of type signatures of radius d with threshold t such that the values (#Type1 ,...,#Typen ) are counted only upto a threshold t and anything ≥ t is considered ∞. Two structures A and B, are said to be d-equivalent with threshold t if their type signatures with ...
... Given d,t ∈ N, we can define the concept of type signatures of radius d with threshold t such that the values (#Type1 ,...,#Typen ) are counted only upto a threshold t and anything ≥ t is considered ∞. Two structures A and B, are said to be d-equivalent with threshold t if their type signatures with ...
logic for computer science - Institute for Computing and Information
... Gottlob Frege, a German mathematician working in relative obscurity. Frege aimed to derive all of mathematics from logical principles, in other words pure reason, together with some self-evident truths about sets. (Such as 'sets are identical if they have the same members' or 'every property determi ...
... Gottlob Frege, a German mathematician working in relative obscurity. Frege aimed to derive all of mathematics from logical principles, in other words pure reason, together with some self-evident truths about sets. (Such as 'sets are identical if they have the same members' or 'every property determi ...
SEQUENT SYSTEMS FOR MODAL LOGICS
... are referred to [Gabbay, 1996], [Goré, 1999] and [Pliuškeviene, 1998]. Also Orlowska’s [1988; 1996] Rasiowa-Sikorski-style relational proof systems for normal modal logics will not be considered in the present chapter. In relational proof systems the logical object language is associated with a la ...
... are referred to [Gabbay, 1996], [Goré, 1999] and [Pliuškeviene, 1998]. Also Orlowska’s [1988; 1996] Rasiowa-Sikorski-style relational proof systems for normal modal logics will not be considered in the present chapter. In relational proof systems the logical object language is associated with a la ...
Dialectica Interpretations A Categorical Analysis
... When Gödel finally1 published his functional interpretation in the journal Dialectica, hence the name “Dialectica Interpretation”, in 1958, it was as a contribution to Hilbert’s program. The Dialectica interpretation reduces consistency of Heyting arithmetic (and combined with the double negation tr ...
... When Gödel finally1 published his functional interpretation in the journal Dialectica, hence the name “Dialectica Interpretation”, in 1958, it was as a contribution to Hilbert’s program. The Dialectica interpretation reduces consistency of Heyting arithmetic (and combined with the double negation tr ...
Thesis Proposal: A Logical Foundation for Session-based
... In Section 3 I develop the interpretation of linear logic as session types that serves as the basis for my work. It has a few variations from that of [5] in that it does not commit to the π-calculus a priori, developing a proof term assignment that can be used as a language for session-typed communi ...
... In Section 3 I develop the interpretation of linear logic as session types that serves as the basis for my work. It has a few variations from that of [5] in that it does not commit to the π-calculus a priori, developing a proof term assignment that can be used as a language for session-typed communi ...
Conjecture
... RWD(G) CWD(G), CWD(H) 2 RWD(G)+1-1 What are the maximum and minimum values of CWD(H) ? Can one characterize the graphs that realize these values ? ...
... RWD(G) CWD(G), CWD(H) 2 RWD(G)+1-1 What are the maximum and minimum values of CWD(H) ? Can one characterize the graphs that realize these values ? ...
Propositional Logic
... proofs or refutations. This use of a logical language is called proof theory. In this case, a set of facts called axioms and a set of deduction rules (inference rules) are given, and the object is to determine which facts follow from the axioms and the rules of inference. When using logic as a proof ...
... proofs or refutations. This use of a logical language is called proof theory. In this case, a set of facts called axioms and a set of deduction rules (inference rules) are given, and the object is to determine which facts follow from the axioms and the rules of inference. When using logic as a proof ...
Truth-Functional Propositional Logic
... the substitution of simple symbols for words. The examples to have in mind are the rules and operations employed in arithmetic and High School algebra. Once we learn how to add, subtract, multiply, and divide the whole numbers {0,1,2,3,...} in elementary school, we can apply these rules, say, to cal ...
... the substitution of simple symbols for words. The examples to have in mind are the rules and operations employed in arithmetic and High School algebra. Once we learn how to add, subtract, multiply, and divide the whole numbers {0,1,2,3,...} in elementary school, we can apply these rules, say, to cal ...
Uniform satisfiability in PSPACE for local temporal logics over
... modalities are definable in monadic second order logic (MSO) are decidable in PSPACE. In this result, we assumed that the architecture of the system is not part of the input which consists of the formula only. Since the complexity also depends on the architecture of the system, it is important to st ...
... modalities are definable in monadic second order logic (MSO) are decidable in PSPACE. In this result, we assumed that the architecture of the system is not part of the input which consists of the formula only. Since the complexity also depends on the architecture of the system, it is important to st ...
CHAPTER 7 GENERAL PROOF SYSTEMS 1 Introduction
... theorems being its final products. The starting points are called axioms of the system. We distinguish two kinds of axioms: logical LA and specific SX. When building a proof system for a given language and its semantics i.e. for a logic defined semantically we choose as a set of logical axioms LA so ...
... theorems being its final products. The starting points are called axioms of the system. We distinguish two kinds of axioms: logical LA and specific SX. When building a proof system for a given language and its semantics i.e. for a logic defined semantically we choose as a set of logical axioms LA so ...
1 Non-deterministic Phase Semantics and the Undecidability of
... generally a separation algebra in the case of Abstract Separation Logic [Calcagno et al. 2007]; see also [Larchey-Wendling and Galmiche 2009] for a general discussion on these links. The Hilbert proof-system of BBI was proved complete w.r.t. relational (or non-deterministic) Kripke semantics [Galmic ...
... generally a separation algebra in the case of Abstract Separation Logic [Calcagno et al. 2007]; see also [Larchey-Wendling and Galmiche 2009] for a general discussion on these links. The Hilbert proof-system of BBI was proved complete w.r.t. relational (or non-deterministic) Kripke semantics [Galmic ...
Formale Methoden der Softwaretechnik Formal methods of software
... Propositional Logic Formal Proofs in Fitch The rule system of Fitch (natural deduction) ...
... Propositional Logic Formal Proofs in Fitch The rule system of Fitch (natural deduction) ...
full text
... propositional logic C2. It is worth noticing that Łukasiewicz two-valued logic Ł2 is nothing else than C2. It means that all Łukasiewicz many-valued logics are generalizations of C2. Chapter II describes the origin and development of Łukasiewicz three-valued logic Ł3 and indicates the connection bet ...
... propositional logic C2. It is worth noticing that Łukasiewicz two-valued logic Ł2 is nothing else than C2. It means that all Łukasiewicz many-valued logics are generalizations of C2. Chapter II describes the origin and development of Łukasiewicz three-valued logic Ł3 and indicates the connection bet ...
Consequence Operators for Defeasible - SeDiCI
... a given theory are preserved when the theory is augmented with new defeasible information. Next we show that semi-monotonicity holds for j»Arg . Proposition 4.4 (Semi-monotonicity). The operator Carg (¡ ) satisfy semi-monotonicity, i:e: Carg (¡ ) µ C arg (¡ [ ¡ 0 ), where ¡ 0 is a theory involving o ...
... a given theory are preserved when the theory is augmented with new defeasible information. Next we show that semi-monotonicity holds for j»Arg . Proposition 4.4 (Semi-monotonicity). The operator Carg (¡ ) satisfy semi-monotonicity, i:e: Carg (¡ ) µ C arg (¡ [ ¡ 0 ), where ¡ 0 is a theory involving o ...
The Bang-Bang Funnel Controller (long version)
... assumptions are very similar when U± are the bounds from the input saturation. The key advantages of the bang-bang funnel controller in comparison to classical controllers are, firstly, the same advantages the continuous funnel controller from [1] has: no knowledge of the systems parameters is neces ...
... assumptions are very similar when U± are the bounds from the input saturation. The key advantages of the bang-bang funnel controller in comparison to classical controllers are, firstly, the same advantages the continuous funnel controller from [1] has: no knowledge of the systems parameters is neces ...
Intuitionistic completeness part I
... and its efficient implementation made rigorous by researchers in programming languages. Our operational semantics of evidence terms follows the method of structured operational semantics of Plotkin [40, 41]. The few basic results about programming language semantics we mention can be found in the co ...
... and its efficient implementation made rigorous by researchers in programming languages. Our operational semantics of evidence terms follows the method of structured operational semantics of Plotkin [40, 41]. The few basic results about programming language semantics we mention can be found in the co ...
Logic in Nonmonotonic Reasoning
... wholesale theories about the world and acting in accordance with them. Both commonsense and nonmonotonic reasoning are just special forms of a general scientific methodology in this sense. The way of thinking in partially known circumstances suggested by nonmonotonic reasoning consists in using rea ...
... wholesale theories about the world and acting in accordance with them. Both commonsense and nonmonotonic reasoning are just special forms of a general scientific methodology in this sense. The way of thinking in partially known circumstances suggested by nonmonotonic reasoning consists in using rea ...
High True vs. Low True Logic
... – Logic 0 could be represented by a LOW voltage (high true) – Logic 0 could be represented by a HIGH voltage (low true) BR 1/99 ...
... – Logic 0 could be represented by a LOW voltage (high true) – Logic 0 could be represented by a HIGH voltage (low true) BR 1/99 ...
The Foundations
... is true ? => The proposition:” It_is_raining” is true iff the condition (or fact) that the sentence is intended to state really occurs(happens, exists) in the situation which the proposition is intended to describe. =>Example: Since it is not raining now(the current situation), the statement It_is_r ...
... is true ? => The proposition:” It_is_raining” is true iff the condition (or fact) that the sentence is intended to state really occurs(happens, exists) in the situation which the proposition is intended to describe. =>Example: Since it is not raining now(the current situation), the statement It_is_r ...
Proof analysis beyond geometric theories: from rule systems to
... The applicability of the method of proof analysis to logics characterized by a relational semantics has brought a wealth of applications to the proof theory of non-classican logics, including provability logic (Negri 2005), substructural logic (Negri 2008), intermediate logics (Dyckhoff and Negri 20 ...
... The applicability of the method of proof analysis to logics characterized by a relational semantics has brought a wealth of applications to the proof theory of non-classican logics, including provability logic (Negri 2005), substructural logic (Negri 2008), intermediate logics (Dyckhoff and Negri 20 ...
Programming in Logic Without Logic Programming
... KELPS is a first-order, sorted language, including a sort for time. In the version of KELPS presented in this paper, we assume that time is linear and discrete, and that the succession of timepoints is represented by the ticks of a logical clock, where 1, 2, ... stand for s(0), s(s(0)), …., t+1 stan ...
... KELPS is a first-order, sorted language, including a sort for time. In the version of KELPS presented in this paper, we assume that time is linear and discrete, and that the succession of timepoints is represented by the ticks of a logical clock, where 1, 2, ... stand for s(0), s(s(0)), …., t+1 stan ...