365 research outputs found
Contract agreements via logic
We relate two contract models: one based on event structures and game theory,
and the other one based on logic. In particular, we show that the notions of
agreement and winning strategies in the game-theoretic model are related to
that of provability in the logical model.Comment: In Proceedings ICE 2013, arXiv:1310.401
Uniform interpolation and coherence
A variety V is said to be coherent if any finitely generated subalgebra of a
finitely presented member of V is finitely presented. It is shown here that V
is coherent if and only if it satisfies a restricted form of uniform deductive
interpolation: that is, any compact congruence on a finitely generated free
algebra of V restricted to a free algebra over a subset of the generators is
again compact. A general criterion is obtained for establishing failures of
coherence, and hence also of uniform deductive interpolation. This criterion is
then used in conjunction with properties of canonical extensions to prove that
coherence and uniform deductive interpolation fail for certain varieties of
Boolean algebras with operators (in particular, algebras of modal logic K and
its standard non-transitive extensions), double-Heyting algebras, residuated
lattices, and lattices
The Grail theorem prover: Type theory for syntax and semantics
As the name suggests, type-logical grammars are a grammar formalism based on
logic and type theory. From the prespective of grammar design, type-logical
grammars develop the syntactic and semantic aspects of linguistic phenomena
hand-in-hand, letting the desired semantics of an expression inform the
syntactic type and vice versa. Prototypical examples of the successful
application of type-logical grammars to the syntax-semantics interface include
coordination, quantifier scope and extraction.This chapter describes the Grail
theorem prover, a series of tools for designing and testing grammars in various
modern type-logical grammars which functions as a tool . All tools described in
this chapter are freely available
Interpolation in extensions of first-order logic
We prove a generalization of Maehara's lemma to show that the extensions of
classical and intuitionistic first-order logic with a special type of geometric
axioms, called singular geometric axioms, have Craig's interpolation property.
As a corollary, we obtain a direct proof of interpolation for (classical and
intuitionistic) first-order logic with identity, as well as interpolation for
several mathematical theories, including the theory of equivalence relations,
(strict) partial and linear orders, and various intuitionistic order theories
such as apartness and positive partial and linear orders.Comment: In this up-dated version of the paper a more general notion of
singular geometric theory is provided allowing the extension of our
interpolation results to further fundamental mathematical theorie
Interpolation in Extensions of First-Order Logic
We prove a generalization of Maehara\u2019s lemma to show that the extensions
of classical and intuitionistic first-order logic with a special type of geometric axioms,
called singular geometric axioms, have Craig\u2019s interpolation property. As a corollary, we
obtain a direct proof of interpolation for (classical and intuitionistic) first-order logic with
identity, as well as interpolation for several mathematical theories, including the theory
of equivalence relations, (strict) partial and linear orders, and various intuitionistic order
theories such as apartness and positive partial and linear orders
Paradeduction in Axiomatic Formal Systems
The concept of paradeduction is presented in order to justify that we can
overlook contradictory information taking into account only what is consistent.
Besides that, paradeduction is used to show that there is a way to transform
any logic, introduced as an axiomatic formal system, into a paraconsistent one
- …