Abella: A System for Reasoning about Relational Specifications
... Types in Abella are the simple types; such types are either primitive types or built from two types using the arrow type constructor →. The type constructor → associates to the right, so every type in Abella can be written in the form τ1 → · · · → τn → b (for n ≥ 0) where b is an atomic type that is ...
... Types in Abella are the simple types; such types are either primitive types or built from two types using the arrow type constructor →. The type constructor → associates to the right, so every type in Abella can be written in the form τ1 → · · · → τn → b (for n ≥ 0) where b is an atomic type that is ...
Introduction to Modal and Temporal Logic
... Classical (Two-Valued) Nature of Kripke Semantics Lemma 1 For any Kripke model hW, R, ϑi, any w ∈ W and any formula ϕ, either ϑ(w, ϕ) = t or else ϑ(w, ϕ) = f . Proof: Pick any Kripke model hW, R, ϑi, any w ∈ W , and any formula ϕ. Proceed by induction on the length l of ϕ. Base Case l = 1: If ϕ is ...
... Classical (Two-Valued) Nature of Kripke Semantics Lemma 1 For any Kripke model hW, R, ϑi, any w ∈ W and any formula ϕ, either ϑ(w, ϕ) = t or else ϑ(w, ϕ) = f . Proof: Pick any Kripke model hW, R, ϑi, any w ∈ W , and any formula ϕ. Proceed by induction on the length l of ϕ. Base Case l = 1: If ϕ is ...
Goal-directed Proof Theory
... S and check by the theorem prover whether ; ^ S ! A. Again, no matter how it is ecient our theorem-prover, it is obvious that there are better methods of performing this task, for instance one attempts a proof of A from ; and determine as far as the proof proceeds what should be added to ; (i.e. a ...
... S and check by the theorem prover whether ; ^ S ! A. Again, no matter how it is ecient our theorem-prover, it is obvious that there are better methods of performing this task, for instance one attempts a proof of A from ; and determine as far as the proof proceeds what should be added to ; (i.e. a ...
A causal approach to nonmonotonic reasoning
... of belief, or consistency, with respect to candidate belief sets (cf. the introductory sections of [33]). It seems that this modal formulation of many nonmonotonic formalisms is mainly due to historical reasons: at the time these formalisms have emerged, modal logics already reigned in the literatur ...
... of belief, or consistency, with respect to candidate belief sets (cf. the introductory sections of [33]). It seems that this modal formulation of many nonmonotonic formalisms is mainly due to historical reasons: at the time these formalisms have emerged, modal logics already reigned in the literatur ...
An Institution-Independent Generalization of Tarski`s Elementary
... properties usually approachable by means of elementary chains, such as Craig interpolation or axiomatizability, are crucial. Institutions are abstract logical frameworks which provide a category of signatures (languages) and signature morphisms (language translations), and, for each signature, a se ...
... properties usually approachable by means of elementary chains, such as Craig interpolation or axiomatizability, are crucial. Institutions are abstract logical frameworks which provide a category of signatures (languages) and signature morphisms (language translations), and, for each signature, a se ...
Preferences and Unrestricted Rebut
... papers is the work of Caminada and Amgoud [2], in which a number of rationality postulates are specified: direct consistency, indirect consistency, (conclusion) closure and subargument closure. The authors provide two different approaches for satisfying these postulates: one that applies unrestricte ...
... papers is the work of Caminada and Amgoud [2], in which a number of rationality postulates are specified: direct consistency, indirect consistency, (conclusion) closure and subargument closure. The authors provide two different approaches for satisfying these postulates: one that applies unrestricte ...
Harmony, Normality and Stability
... with the logical constants. ‘The first category [of principles governing our linguistic practice] consists of those that have to do with the circumstances that warrant an assertion [. . .] we need to know when we are entitled to make any given assertion, and when we are required to acknowledge it as ...
... with the logical constants. ‘The first category [of principles governing our linguistic practice] consists of those that have to do with the circumstances that warrant an assertion [. . .] we need to know when we are entitled to make any given assertion, and when we are required to acknowledge it as ...
On the Complexity of Qualitative Spatial Reasoning: A Maximal
... of RCC-8 relations will be carried out . All of them use a reduction of a propositional satisfiability problem to RSAT(S) by constructing a set of spatial formulas O for every instance Z of the propositional problem. such that O is consistent iff Z is a positive instance . These satisfiability probl ...
... of RCC-8 relations will be carried out . All of them use a reduction of a propositional satisfiability problem to RSAT(S) by constructing a set of spatial formulas O for every instance Z of the propositional problem. such that O is consistent iff Z is a positive instance . These satisfiability probl ...
Completeness theorems and lambda
... What happens if one restricts system F to the subsystem F0 where one allows only to form ΠX.T (X) if T (X) is built only with X and →?? Can one use the techniques of proof theory and give a predicative normalisation proof for this fragment? I. Takeuti gave such a proof in 1993, following G. Takeuti, ...
... What happens if one restricts system F to the subsystem F0 where one allows only to form ΠX.T (X) if T (X) is built only with X and →?? Can one use the techniques of proof theory and give a predicative normalisation proof for this fragment? I. Takeuti gave such a proof in 1993, following G. Takeuti, ...
Making Abstract Domains Condensing
... program for a fixed query with a given initial description. On the other hand, a goal-independent analyzer computes information on a program P for all the possible initial queries for P , and then this whole abstract semantics allows to derive the information of the analysis for a particular query. ...
... program for a fixed query with a given initial description. On the other hand, a goal-independent analyzer computes information on a program P for all the possible initial queries for P , and then this whole abstract semantics allows to derive the information of the analysis for a particular query. ...
a semantic perspective - Institute for Logic, Language and
... of algebraic semantics) the best explored style of modal semantics. It is also, arguably, the most intuitive. Over the years modal logic has been applied in many different ways. It has been used as a tool for reasoning about time, beliefs, computational systems, necessity and possibility, and much e ...
... of algebraic semantics) the best explored style of modal semantics. It is also, arguably, the most intuitive. Over the years modal logic has been applied in many different ways. It has been used as a tool for reasoning about time, beliefs, computational systems, necessity and possibility, and much e ...
5 model theory of modal logic
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related t ...
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related t ...
Modular Construction of Complete Coalgebraic Logics
... Replacing the unbounded powerset functor by the finite powerset functor in these definitions yields image-finite variants of these two types of systems. The image-finite simple probabilistic automata are called probabilistic transition systems in [12]. Note that all the endofunctors in the previous ...
... Replacing the unbounded powerset functor by the finite powerset functor in these definitions yields image-finite variants of these two types of systems. The image-finite simple probabilistic automata are called probabilistic transition systems in [12]. Note that all the endofunctors in the previous ...
A Computationally-Discovered Simplification of the Ontological
... greater can be conceived’ into universal claims without first establishing that there is something which is the thing than which nothing greater can be conceived. Note also that in free logic, the following two axioms (the second is an axiom schema) are logical truths (i.e., true in every classical ...
... greater can be conceived’ into universal claims without first establishing that there is something which is the thing than which nothing greater can be conceived. Note also that in free logic, the following two axioms (the second is an axiom schema) are logical truths (i.e., true in every classical ...
A Computationally-Discovered Simplification of the Ontological
... greater can be conceived’ into universal claims without first establishing that there is something which is the thing than which nothing greater can be conceived. Note also that in free logic, the following two axioms (the second is an axiom schema) are logical truths (i.e., true in every classical ...
... greater can be conceived’ into universal claims without first establishing that there is something which is the thing than which nothing greater can be conceived. Note also that in free logic, the following two axioms (the second is an axiom schema) are logical truths (i.e., true in every classical ...
Curry-Howard Isomorphism - Department of information engineering
... In both cases a somewhat rare presentation—taken from Prawitz—with assumptions as sets, not sequences, is adopted. For the intuitionistic system the cut-elimination theorem is mentioned, and from this the subformula property and decidability of the logic are inferred. Two aproaches to term assignmen ...
... In both cases a somewhat rare presentation—taken from Prawitz—with assumptions as sets, not sequences, is adopted. For the intuitionistic system the cut-elimination theorem is mentioned, and from this the subformula property and decidability of the logic are inferred. Two aproaches to term assignmen ...
On perturbations of continuous structures - HAL
... Abstract. We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are approximately ω-saturated up to arbitrarily small ...
... Abstract. We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are approximately ω-saturated up to arbitrarily small ...
MoL-2013-07 - Institute for Logic, Language and Computation
... theory, prove some characterisation results for it, and then piggyback on the results of [HL13] to show that this modal theory is exactly the one corresponding to the modal logic of inner models. The result which allows us to do this is that the relation ‘being a forcing ground’ is an initial segmen ...
... theory, prove some characterisation results for it, and then piggyback on the results of [HL13] to show that this modal theory is exactly the one corresponding to the modal logic of inner models. The result which allows us to do this is that the relation ‘being a forcing ground’ is an initial segmen ...
Notes on the Science of Logic
... that every formula contains at most a finite number of atomic symbols—you can “see” that this must be so. These notes will rely on no such “vision,” but will instead analyze the principles lying behind such intuitions so that for justifying proofs the intuitions themselves can be dispensed with. Wit ...
... that every formula contains at most a finite number of atomic symbols—you can “see” that this must be so. These notes will rely on no such “vision,” but will instead analyze the principles lying behind such intuitions so that for justifying proofs the intuitions themselves can be dispensed with. Wit ...
ON PERTURBATIONS OF CONTINUOUS STRUCTURES
... Abstract. We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are approximately ω-saturated up to arbitrarily small ...
... Abstract. We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are approximately ω-saturated up to arbitrarily small ...
Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
Artificial Intelligence
... km/h, but the linguistic variable stopping_distance can take either value long or short. In other words, classical rules are expressed in the black-and-white language of Boolean logic. ...
... km/h, but the linguistic variable stopping_distance can take either value long or short. In other words, classical rules are expressed in the black-and-white language of Boolean logic. ...
Independence logic and tuple existence atoms
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
Consequence relations and admissible rules
... weakening if Γ ` ∆, then Γ0 , Γ ` ∆, ∆0 , transitivity if Γ ` ∆, A and Γ0 , A ` ∆0 , then Γ0 , Γ ` ∆, ∆0 . For the first and third property we use Scott’s terminology from [14], where multi– conclusion consequence relations of this form are introduced for the first time. The second property is calle ...
... weakening if Γ ` ∆, then Γ0 , Γ ` ∆, ∆0 , transitivity if Γ ` ∆, A and Γ0 , A ` ∆0 , then Γ0 , Γ ` ∆, ∆0 . For the first and third property we use Scott’s terminology from [14], where multi– conclusion consequence relations of this form are introduced for the first time. The second property is calle ...
KURT GÖDEL - National Academy of Sciences
... 1 am endeavoring to give enough background material to enable a scientist who is not a professional mathematician and not already acquainted with mathematical logic to understand Godel's best-known contributions. The memoir (1980) by Kreisel, about three times the length of the present one, includes ...
... 1 am endeavoring to give enough background material to enable a scientist who is not a professional mathematician and not already acquainted with mathematical logic to understand Godel's best-known contributions. The memoir (1980) by Kreisel, about three times the length of the present one, includes ...