Consequence relations and admissible rules
... for a sentence A to logically follow from a set of sentences Γ. He arrived at the definition that this is so if and only if every model of the sentences in Γ is a model of A. This led to the introduction and study of consequence relations, which are relations between sets of expressions and expressi ...
... for a sentence A to logically follow from a set of sentences Γ. He arrived at the definition that this is so if and only if every model of the sentences in Γ is a model of A. This led to the introduction and study of consequence relations, which are relations between sets of expressions and expressi ...
The Herbrand Manifesto
... weaker. In fact, it is stronger. There are more things that are true. We cannot prove them all, but we can prove everything we could prove before. Some may be disturbed by the fact that Herbrand entailment is not semi-decidable. But a similar argument could be leveled against Tarskian semantics. Sem ...
... weaker. In fact, it is stronger. There are more things that are true. We cannot prove them all, but we can prove everything we could prove before. Some may be disturbed by the fact that Herbrand entailment is not semi-decidable. But a similar argument could be leveled against Tarskian semantics. Sem ...
A logic-based theory of deductive arguments
... by which the conclusion is meant to follow from the reasons. The nature of inference is diverse and includes analogical inference, causal inference, and inductive inference. We focus on deductive inference and hence on deductive arguments, i.e., the conclusion is a deductively valid consequence of t ...
... by which the conclusion is meant to follow from the reasons. The nature of inference is diverse and includes analogical inference, causal inference, and inductive inference. We focus on deductive inference and hence on deductive arguments, i.e., the conclusion is a deductively valid consequence of t ...
Self-Referential Probability
... on a supervaluational evaluation scheme. This variation is particularly interesting because it bears a close relationship to imprecise probabilities where agents’ credal states are taken to be sets of probability functions. In this chapter, we will also consider how to use this language to describe ...
... on a supervaluational evaluation scheme. This variation is particularly interesting because it bears a close relationship to imprecise probabilities where agents’ credal states are taken to be sets of probability functions. In this chapter, we will also consider how to use this language to describe ...
Many-Valued Logic
... Suppose we were to retain the obvious classical clauses: v (¬A ) = 1 ⇔ v (A ) = 0 v (¬A ) = 0 ⇔ v (A ) = 1 v (A ∧ B ) = 1 ⇔ v (A ) = v (B ) = 1 v (A ∧ B ) = 0 ⇔ v (A ) = 0 or v (B ) = 0 v (A ∨ B ) = 1 ⇔ v (A ) = 1 or v (B ) = 1 v (A ∨ B ) = 0 ⇔ v (A ) = v (B ) = 0 v (A ⊃ B ) = 1 ⇔ v (A ) = 0 or v (B ...
... Suppose we were to retain the obvious classical clauses: v (¬A ) = 1 ⇔ v (A ) = 0 v (¬A ) = 0 ⇔ v (A ) = 1 v (A ∧ B ) = 1 ⇔ v (A ) = v (B ) = 1 v (A ∧ B ) = 0 ⇔ v (A ) = 0 or v (B ) = 0 v (A ∨ B ) = 1 ⇔ v (A ) = 1 or v (B ) = 1 v (A ∨ B ) = 0 ⇔ v (A ) = v (B ) = 0 v (A ⊃ B ) = 1 ⇔ v (A ) = 0 or v (B ...
Justifying Underlying Desires for Argument
... their individual problems on negotiation. However, determining agent’s underlying desires behind the given goals or proposals, or revising them is outside the scope of these literatures. In [8–10], the authors give mechanisms for generating knowledge-dependent and context-dependent desires in practi ...
... their individual problems on negotiation. However, determining agent’s underlying desires behind the given goals or proposals, or revising them is outside the scope of these literatures. In [8–10], the authors give mechanisms for generating knowledge-dependent and context-dependent desires in practi ...
Introduction to Linear Logic
... and the remaining rules are subject to the restriction that each right hand side context contains exactly one formula. We shall here consider also an equivalent Natural Deduction presentation of Intuitionistic Logic which has cleaner dynamic properties than the presentation in Gentzen style. Proof-r ...
... and the remaining rules are subject to the restriction that each right hand side context contains exactly one formula. We shall here consider also an equivalent Natural Deduction presentation of Intuitionistic Logic which has cleaner dynamic properties than the presentation in Gentzen style. Proof-r ...
A Logical Foundation for Session
... Over the years, computation systems have evolved from monolithic single-threaded machines to concurrent and distributed environments with multiple communicating threads of execution, for which writing correct programs becomes substantially harder than in the more traditional sequential setting. Thes ...
... Over the years, computation systems have evolved from monolithic single-threaded machines to concurrent and distributed environments with multiple communicating threads of execution, for which writing correct programs becomes substantially harder than in the more traditional sequential setting. Thes ...
Relevant and Substructural Logics
... collections as premises, to a conclusion. This is because lists or other structures can distinguish the order or quantity of individual premises, while sets cannot. However, this is all that can simply be done to define consequence relations within the confines of a Hilbert system, so here is where ...
... collections as premises, to a conclusion. This is because lists or other structures can distinguish the order or quantity of individual premises, while sets cannot. However, this is all that can simply be done to define consequence relations within the confines of a Hilbert system, so here is where ...
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 ...
Problems on Discrete Mathematics1 (Part I)
... correct. But, in general, we are not able to do so because the domain is usually an infinite set, and even worse, the domain can be uncountable, e.g., real numbers. To overcome this problem, we divide the domain into several categories and make sure that those categories cover the domain. Then we ex ...
... correct. But, in general, we are not able to do so because the domain is usually an infinite set, and even worse, the domain can be uncountable, e.g., real numbers. To overcome this problem, we divide the domain into several categories and make sure that those categories cover the domain. Then we ex ...
Logic in Nonmonotonic Reasoning
... than on traditional logical tools. Nevertheless, it has managed to provide a plausible analysis of reasoning in this restricted context. Nonmonotonic reasoning of a different kind has been observed in the framework of already existing systems, such as databases, logic programming and planning algori ...
... than on traditional logical tools. Nevertheless, it has managed to provide a plausible analysis of reasoning in this restricted context. Nonmonotonic reasoning of a different kind has been observed in the framework of already existing systems, such as databases, logic programming and planning algori ...
Programming in Logic Without Logic Programming
... 0 of the state Si to which the fluent belongs. The unstamped fluent atom p(t1, …, tn) is the same atom without this timestamp. Event predicates represent events contributing to the transition from one state to the next. The last argument of a timestamped event atom e(t1, …, tn, i) is a time paramete ...
... 0 of the state Si to which the fluent belongs. The unstamped fluent atom p(t1, …, tn) is the same atom without this timestamp. Event predicates represent events contributing to the transition from one state to the next. The last argument of a timestamped event atom e(t1, …, tn, i) is a time paramete ...
In order to define the notion of proof rigorously, we would have to
... P ⇒⊥ and to abbreviate it as ¬P (or sometimes ∼ P ). Thus, ¬P (say: not P ) is just a shorthand for P ⇒⊥. This interpretation of negation may be confusing at first. The intuitive idea is that ¬P = (P ⇒⊥) is true if and only if P is not true because if both P and P ⇒⊥ were true then we could conclude ...
... P ⇒⊥ and to abbreviate it as ¬P (or sometimes ∼ P ). Thus, ¬P (say: not P ) is just a shorthand for P ⇒⊥. This interpretation of negation may be confusing at first. The intuitive idea is that ¬P = (P ⇒⊥) is true if and only if P is not true because if both P and P ⇒⊥ were true then we could conclude ...
Foundations for Knowledge
... In this paper we develop a new foundation for knowledgebased programs by using the recently proposed variant of the situation calculus called ES (Lakemeyer & Levesque 2004). It does not use situation terms in the language and hence can directly serve as the language for tests. In fact, the tests in ...
... In this paper we develop a new foundation for knowledgebased programs by using the recently proposed variant of the situation calculus called ES (Lakemeyer & Levesque 2004). It does not use situation terms in the language and hence can directly serve as the language for tests. In fact, the tests in ...
Forking in simple theories and CM-triviality Daniel Palacín Cruz
... question is still open for small simple theories. In addition, there is an example of a theory without the strict order property which does not eliminate hyperimaginaries [18]. It is worth remarkable a theorem due to Lascar and Pillay showing that every bounded hyperimaginary can be replaced in favo ...
... question is still open for small simple theories. In addition, there is an example of a theory without the strict order property which does not eliminate hyperimaginaries [18]. It is worth remarkable a theorem due to Lascar and Pillay showing that every bounded hyperimaginary can be replaced in favo ...
Intuitionistic completeness part I
... not constructively valid. We take a very different approach, effectively converting uniform evidence for validity into a proof. We do this by building objects called evidence structures that reveal the evidence term layer by layer. For instance, when we see evidence of the form λ(x.b(x)) for a formu ...
... not constructively valid. We take a very different approach, effectively converting uniform evidence for validity into a proof. We do this by building objects called evidence structures that reveal the evidence term layer by layer. For instance, when we see evidence of the form λ(x.b(x)) for a formu ...
Propositional inquisitive logic: a survey
... non-standard connective. In this section we will show that if, on the other hand, we regard as the standard disjunction of the system, then InqB turns out to be a special kind of intermediate logic, i.e., a logic sitting in between intuitionistic and classical logic. The first step in this direction ...
... non-standard connective. In this section we will show that if, on the other hand, we regard as the standard disjunction of the system, then InqB turns out to be a special kind of intermediate logic, i.e., a logic sitting in between intuitionistic and classical logic. The first step in this direction ...
Discrete Mathematics for Computer Science Some Notes
... is. To do this, one has to define precisely what are the “rules of mathematical reasoning” and this is a lot harder than it looks. Of course, defining and analyzing the notion of proof is a major goal of mathematical logic. Having attempted some twenty years ago to “demystify” logic for computer sci ...
... is. To do this, one has to define precisely what are the “rules of mathematical reasoning” and this is a lot harder than it looks. Of course, defining and analyzing the notion of proof is a major goal of mathematical logic. Having attempted some twenty years ago to “demystify” logic for computer sci ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... modal logic of weak and strict preference interpreted in ordered models of possible worlds, we discuss its expressive power and we provide a complete axiomatization. In particular, we show how this language can define global preferences between propositions, by lifting the world ordering to an order ...
... modal logic of weak and strict preference interpreted in ordered models of possible worlds, we discuss its expressive power and we provide a complete axiomatization. In particular, we show how this language can define global preferences between propositions, by lifting the world ordering to an order ...
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 ...
Dedukti
... function symbol 7→ that would bind a variable in its argument. 2. Predicate logic ignores the propositions-as-types principle, according to which a proof π of a proposition A is a term of type A. 3. Predicate logic ignores the difference between deduction and computation. For example, when Peano ari ...
... function symbol 7→ that would bind a variable in its argument. 2. Predicate logic ignores the propositions-as-types principle, according to which a proof π of a proposition A is a term of type A. 3. Predicate logic ignores the difference between deduction and computation. For example, when Peano ari ...
A causal approach to nonmonotonic reasoning
... since it is based on a direct and transparent description of factual and causal (explanatory) information about the world. In other words, it shows that the epistemic view of nonmonotonic reasoning is not the only possibility. Accordingly, the primary aim of our study will consist in laying down log ...
... since it is based on a direct and transparent description of factual and causal (explanatory) information about the world. In other words, it shows that the epistemic view of nonmonotonic reasoning is not the only possibility. Accordingly, the primary aim of our study will consist in laying down log ...
relevance logic - Consequently.org
... and to a lesser extent on [Meyer, 1966], both of which are very much recommended to the reader for their wise heresy from logical tradition. Thus logical tradition (think of [Quine, 1953]) makes much of the grammatical distinction between ‘if, then’ (a connective), and ‘implies’ or its rough synonym ...
... and to a lesser extent on [Meyer, 1966], both of which are very much recommended to the reader for their wise heresy from logical tradition. Thus logical tradition (think of [Quine, 1953]) makes much of the grammatical distinction between ‘if, then’ (a connective), and ‘implies’ or its rough synonym ...
HOW TO DEFINE A MEREOLOGICAL (COLLECTIVE) SET
... properties of sets in mathematics and differences between them and so called conglomerates in Section 1, we go on to explicate informally in Section 2 what it means to join many objects into a single entity from point of view of mereology, the theory of part of (parthood) relation. In Section 3 we pr ...
... properties of sets in mathematics and differences between them and so called conglomerates in Section 1, we go on to explicate informally in Section 2 what it means to join many objects into a single entity from point of view of mereology, the theory of part of (parthood) relation. In Section 3 we pr ...