Finite satisfiability for guarded fixpoint logic
... the node labels of v 0 and v 1 are the same. Also, for any i ∈ {0, 1} and node w i connected to v i by an edge, there exits a node w 1−i connected to v 1−i by an edge and such that ( w 0 , w 1 ) ∈ Z . We say that node v 0 of a graph G 0 is bisimilar to node v 1 in a graph G 1 if there is an undirect ...
... the node labels of v 0 and v 1 are the same. Also, for any i ∈ {0, 1} and node w i connected to v i by an edge, there exits a node w 1−i connected to v 1−i by an edge and such that ( w 0 , w 1 ) ∈ Z . We say that node v 0 of a graph G 0 is bisimilar to node v 1 in a graph G 1 if there is an undirect ...
MoggiMonads.pdf
... was later extended, following a similar methodology, to consider other features of computations like nondeterminism (see [Sha84]), side-effects and continuations (see [FFKD86, FF89]). The calculi based only on operational considerations, like the λv -calculus, are sound and complete w.r.t. the opera ...
... was later extended, following a similar methodology, to consider other features of computations like nondeterminism (see [Sha84]), side-effects and continuations (see [FFKD86, FF89]). The calculi based only on operational considerations, like the λv -calculus, are sound and complete w.r.t. the opera ...
CS2300-1.7
... • A lemma is a ‘helping theorem’ or a result which is needed to prove a theorem. • A corollary is a result which follows directly from a theorem. • Less important theorems are sometimes called propositions. • A conjecture is a statement that is being proposed to be true. Once a proof of a conjecture ...
... • A lemma is a ‘helping theorem’ or a result which is needed to prove a theorem. • A corollary is a result which follows directly from a theorem. • Less important theorems are sometimes called propositions. • A conjecture is a statement that is being proposed to be true. Once a proof of a conjecture ...
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 ...
Diagrammatic Reasoning in Separation Logic
... proof sch-pf would be a function of the length of the list, such that sch-pf (n) is a proof that lists specifically of length n are reversed by the program. A disadvantage of this approach is that it requires at least one example proof from the user in every case. Possible future work would be to lo ...
... proof sch-pf would be a function of the length of the list, such that sch-pf (n) is a proof that lists specifically of length n are reversed by the program. A disadvantage of this approach is that it requires at least one example proof from the user in every case. Possible future work would be to lo ...
Algebraic Proof Complexity: Progress, Frontiers and Challenges
... each yj and zi , then this is a linear IPS refutation (called basically Hilbert IPS by GrochowPitassi [Grochow and Pitassi, 2014]), which is abbreviated as IPS LIN . If C comes from a restricted class of algebraic circuits C, then this is called a C-IPS refutation, and further called a C-IPSLIN refu ...
... each yj and zi , then this is a linear IPS refutation (called basically Hilbert IPS by GrochowPitassi [Grochow and Pitassi, 2014]), which is abbreviated as IPS LIN . If C comes from a restricted class of algebraic circuits C, then this is called a C-IPS refutation, and further called a C-IPSLIN refu ...
Strong Logics of First and Second Order
... We begin by recalling some basic features of first-order logic. Let L be a first-order language. The relation of logical implication is defined as follows: For T a recursively enumerable3 set of sentences in L and ϕ a sentence in L, T |= ϕ iff for every L-structure M, if M |= T then M |= ϕ. This rel ...
... We begin by recalling some basic features of first-order logic. Let L be a first-order language. The relation of logical implication is defined as follows: For T a recursively enumerable3 set of sentences in L and ϕ a sentence in L, T |= ϕ iff for every L-structure M, if M |= T then M |= ϕ. This rel ...
AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY
... began with Carnap (1946, 1947), where he presented a semantics for logical necessity based on Leibniz’s old idea that a proposition is necessarily true if and only if it is true in all possible worlds. In his formal semantics, Carnap used syntactic entities — state-descriptions — as representatives ...
... began with Carnap (1946, 1947), where he presented a semantics for logical necessity based on Leibniz’s old idea that a proposition is necessarily true if and only if it is true in all possible worlds. In his formal semantics, Carnap used syntactic entities — state-descriptions — as representatives ...
How To Do Proofs (for 1B Semantics of Programming Languages)
... The purpose of this handout is give a general guide as to how to prove theorems. This should give you some help in answering questions that begin with “Show that the following is true . . . ”. It is based on notes by Myra VanInwegen, with additional text added by Peter Sewell. The focus here is on d ...
... The purpose of this handout is give a general guide as to how to prove theorems. This should give you some help in answering questions that begin with “Show that the following is true . . . ”. It is based on notes by Myra VanInwegen, with additional text added by Peter Sewell. The focus here is on d ...
Expressive Power of SQL
... The conclusion, of course, is that SQL has more power than relational algebra, and the main source of this additional power is its aggregation and grouping constructs, together with arithmetic operations on numerical attributes. But then one cannot say that the transitive closure query is not expres ...
... The conclusion, of course, is that SQL has more power than relational algebra, and the main source of this additional power is its aggregation and grouping constructs, together with arithmetic operations on numerical attributes. But then one cannot say that the transitive closure query is not expres ...
24.241 Logic I Problem set 04 solutions
... Γ and the conclusion of α is P (I’m using ‘α’ so you don’t confuse it with a sentence letter of SL, but you can use whatever you like). 1. α is valid in SD iff there is an SD derivation that has the members of Γ as primary assumptions and P in the scope of those assumptions only (by definition of ‘va ...
... Γ and the conclusion of α is P (I’m using ‘α’ so you don’t confuse it with a sentence letter of SL, but you can use whatever you like). 1. α is valid in SD iff there is an SD derivation that has the members of Γ as primary assumptions and P in the scope of those assumptions only (by definition of ‘va ...
Acts of Commanding and Changing Obligations
... A word about my choice of monadic deontic operators here may be in order. Monadic deontic logics are known to be inadequate to deal with conditional obligations and R. M. Chisholm’s contrary-to-duty paradox; dyadic deontic logics are better in this respect. But there are still other problems which a ...
... A word about my choice of monadic deontic operators here may be in order. Monadic deontic logics are known to be inadequate to deal with conditional obligations and R. M. Chisholm’s contrary-to-duty paradox; dyadic deontic logics are better in this respect. But there are still other problems which a ...
Dependent Types In Lambda Cube
... sense of the word exists. Other names are also propositions as types, formulas as types or proofs as programs. Each of these names already gives advice on what is the correspondence about. The discovery of the isomorphism is thanks to the American mathematician Haskell Curry and logician William Alv ...
... sense of the word exists. Other names are also propositions as types, formulas as types or proofs as programs. Each of these names already gives advice on what is the correspondence about. The discovery of the isomorphism is thanks to the American mathematician Haskell Curry and logician William Alv ...
A Deduction Method Complete for Refutation and Finite Satis ability
... it satis es, and will therefore be denoted by ( ). If is a set ( nite set, resp.) of formulas and ( ) a term model of , there might be constants ( nitely many constants, resp.) in which do not occur in . These constants are assumed to be interpreted over the special constant c0 which without loss of ...
... it satis es, and will therefore be denoted by ( ). If is a set ( nite set, resp.) of formulas and ( ) a term model of , there might be constants ( nitely many constants, resp.) in which do not occur in . These constants are assumed to be interpreted over the special constant c0 which without loss of ...
