Views: Compositional Reasoning for Concurrent Programs
... state such that this typing is preserved. When views are composed, they must agree on the types of all variables they share. In a type system that permits strong (i.e. type-changing) updates, threads again have knowledge that variables agree with their types, but may make updates that change the typ ...
... state such that this typing is preserved. When views are composed, they must agree on the types of all variables they share. In a type system that permits strong (i.e. type-changing) updates, threads again have knowledge that variables agree with their types, but may make updates that change the typ ...
Mathematical Structures for Reachability Sets and Relations Summary
... Given a vector addition system with states (VASS) and an initial configuration, as usual, the reachability set is defined as the set of all configurations that can be reached from the initial configuration by using the transitions of the VASS. The reachability problem for VASS amounts to checking wh ...
... Given a vector addition system with states (VASS) and an initial configuration, as usual, the reachability set is defined as the set of all configurations that can be reached from the initial configuration by using the transitions of the VASS. The reachability problem for VASS amounts to checking wh ...
Combining Paraconsistent Logic with Argumentation
... cases less expressiveness may suffice, a full theory of the logic of argumentation cannot exclude the general case. Caminada, Carnielli and Dunne [5] formulated a new set of rationality postulates in addition to those of Caminada and Amgoud [3], to characterise cases under which the trivialisation p ...
... cases less expressiveness may suffice, a full theory of the logic of argumentation cannot exclude the general case. Caminada, Carnielli and Dunne [5] formulated a new set of rationality postulates in addition to those of Caminada and Amgoud [3], to characterise cases under which the trivialisation p ...
CS243: Discrete Structures Mathematical Proof Techniques
... exist some integer k such that n = 2k + 1. Then, n 2 = 4k 2 + 4k + 1 = 2(2k 2 + 2k ) + 1, which is odd. Thus, if n is odd, n 2 is also odd. ...
... exist some integer k such that n = 2k + 1. Then, n 2 = 4k 2 + 4k + 1 = 2(2k 2 + 2k ) + 1, which is odd. Thus, if n is odd, n 2 is also odd. ...
Ascribing beliefs to resource bounded agents
... P ROOF. We need to prove that neither of the following consequences holds: Bp1 , ..., Bpn , B¬pn+1 , ..., B¬pn+k |=E Bpi unless i ∈ {1, . . . , n} and Bp1 , ..., Bpn , B¬pn+1 , ..., B¬pn+k |=E B¬pi unless i ∈ {n + 1, . . . , n + k}. The first consequence would hold if for all interpretations of p1 , ...
... P ROOF. We need to prove that neither of the following consequences holds: Bp1 , ..., Bpn , B¬pn+1 , ..., B¬pn+k |=E Bpi unless i ∈ {1, . . . , n} and Bp1 , ..., Bpn , B¬pn+1 , ..., B¬pn+k |=E B¬pi unless i ∈ {n + 1, . . . , n + k}. The first consequence would hold if for all interpretations of p1 , ...
Sketch-as-proof - Norbert Preining
... proof theory and projective geometry. We applied theoretic methods of proof theory to projective geometry. This should be another try to span the gap between theoretical and applied mathematics. The gap arises from the fact, that “applied mathematicians” don’t want to use the methods of proof theory ...
... proof theory and projective geometry. We applied theoretic methods of proof theory to projective geometry. This should be another try to span the gap between theoretical and applied mathematics. The gap arises from the fact, that “applied mathematicians” don’t want to use the methods of proof theory ...
Completeness - OSU Department of Mathematics
... • Whenever f is an n-ary function symbol h(f A (a1 , . . . , an )) = f B (h(a1 ), . . . , h(an )) for all a1 , . . . , an ∈ |A|. Notice that if = is in L, A and B respect equality and h is a homormorphism of A to B then h is 1-1 i.e. h is an embedding of A into B. When h is a homomorphism from A to ...
... • Whenever f is an n-ary function symbol h(f A (a1 , . . . , an )) = f B (h(a1 ), . . . , h(an )) for all a1 , . . . , an ∈ |A|. Notice that if = is in L, A and B respect equality and h is a homormorphism of A to B then h is 1-1 i.e. h is an embedding of A into B. When h is a homomorphism from A to ...
An Introduction to Proof Theory - UCSD Mathematics
... Proof Theory is the area of mathematics which studies the concepts of mathematical proof and mathematical provability. Since the notion of “proof” plays a central role in mathematics as the means by which the truth or falsity of mathematical propositions is established; Proof Theory is, in principle ...
... Proof Theory is the area of mathematics which studies the concepts of mathematical proof and mathematical provability. Since the notion of “proof” plays a central role in mathematics as the means by which the truth or falsity of mathematical propositions is established; Proof Theory is, in principle ...
Loop Formulas for Circumscription - Joohyung Lee
... In logic programming where predicate completion is best known and commonly referred to as program completion semantics, its relationships with other semantics, especially the answer set semantics (also known as the stable model semantics) of Gelfond and Lifschitz [1988], have been studied quite exte ...
... In logic programming where predicate completion is best known and commonly referred to as program completion semantics, its relationships with other semantics, especially the answer set semantics (also known as the stable model semantics) of Gelfond and Lifschitz [1988], have been studied quite exte ...
The definable criterion for definability in Presburger arithmetic and
... rather interesting. If we add to a self-de nable structure new predicates such that the theory of the new structure is decidable then given a formula of the new structure one can e2ectively decide whether this formula is equivalent to some formula of the old structure. Unfortunately, we do not know ...
... rather interesting. If we add to a self-de nable structure new predicates such that the theory of the new structure is decidable then given a formula of the new structure one can e2ectively decide whether this formula is equivalent to some formula of the old structure. Unfortunately, we do not know ...
Logic and Proof Jeremy Avigad Robert Y. Lewis Floris van Doorn
... assistants has begun to make complete formalization feasible. Working interactively with theorem proving software, users can construct formal derivations of complex theorems that can be stored and checked by computer. Automated methods can be used to fill in small gaps by hand, verify long calculatio ...
... assistants has begun to make complete formalization feasible. Working interactively with theorem proving software, users can construct formal derivations of complex theorems that can be stored and checked by computer. Automated methods can be used to fill in small gaps by hand, verify long calculatio ...
Digital Logic and the Control Unit
... functional representation. Note that F2 is 1 if and only if two of X, Y, and Z are 1. Given this, we can give a functional description of the function as F2 = XY + XZ + YZ. As the student might suspect, neither the pattern of 0’s and 1’s for F1 nor that for F2 were arbitrarily selected. The real ...
... functional representation. Note that F2 is 1 if and only if two of X, Y, and Z are 1. Given this, we can give a functional description of the function as F2 = XY + XZ + YZ. As the student might suspect, neither the pattern of 0’s and 1’s for F1 nor that for F2 were arbitrarily selected. The real ...
Modal Logics of Submaximal and Nodec Spaces 1 Introduction
... X is a dense-in-itself door space [7], hence is not an I-space. A space X is called maximal if every open subset of X is infinite and any strictly finer topology on X contains a finite open set. It is known (see, e.g., [13, Theorem 24]) that every maximal space is submaximal. Since maximal spaces ar ...
... X is a dense-in-itself door space [7], hence is not an I-space. A space X is called maximal if every open subset of X is infinite and any strictly finer topology on X contains a finite open set. It is known (see, e.g., [13, Theorem 24]) that every maximal space is submaximal. Since maximal spaces ar ...
Löwenheim-Skolem Theorems, Countable Approximations, and L
... In its simplest form the Löwenheim-Skolem Theorem for Lω1 ω states that if σ ∈ Lω1 ω and M |= σ then M0 |= σ for some (in fact, ‘many’) countable M0 ⊆ M . For sentences in L∞ω but not in Lω1 ω this property normally fails. But we will see that the L∞ω properties of arbitrary structures are determin ...
... In its simplest form the Löwenheim-Skolem Theorem for Lω1 ω states that if σ ∈ Lω1 ω and M |= σ then M0 |= σ for some (in fact, ‘many’) countable M0 ⊆ M . For sentences in L∞ω but not in Lω1 ω this property normally fails. But we will see that the L∞ω properties of arbitrary structures are determin ...
On the strength of the finite intersection principle
... The authors are grateful to Denis Hirschfeldt, Antonio Montalbán, and Robert Soare for valuable comments and suggestions. The first author was partially supported by an NSF Graduate Research Fellowship and an NSF Postdoctoral Fellowship. ...
... The authors are grateful to Denis Hirschfeldt, Antonio Montalbán, and Robert Soare for valuable comments and suggestions. The first author was partially supported by an NSF Graduate Research Fellowship and an NSF Postdoctoral Fellowship. ...